Pair of Linear Equations in Two Variables
Hello friends, How are you doing? I hope you will have been doing good!
Friends me hoon Dheeraj Sahni and you are on my website www.mathshindi.com right now. Aapka bohot bohot swagat hai meri iss website par. Iss website par aapko maths se related complex topic ko easy way me samjhaaya jaata hai aur sirf ye hi nahi wo complex topics aapko acche se samajh me aa jaaye iske liye aapko unn topics se related examples/questions bhi diye jaate hai.
Friends, aaj me aapko batane waala hoon Pair of Linear Equations in Two Variables ke baare me. Iss article mein me aapko bataoonga ki Pair of Linear Equations in Two Variables kya hota hai aur iss type ke equations ko kaise solve karte hain. So friends,
Let's begin...
Pair of Linear Equations in Two Variables ka matlab kya hota hai- ye jaanne se pehle me aapko recommend karna chahoonga ki aap mere iss article- What is polynomial and equation? ko padhe aur dhyaan se samajhe.
Iss article ka link me aapko yaha de raha hoon , iss article ko padhne ke liye iss blue link par click kijiye »»»
[What is polynomial and equation?].
I hope ki aap log iss article ko padhkar polynomials aur equations ke baare me acche se samajh gaye honge.
So friends, chaliye aage badhte hain...
Friends abb baat karte hain aaj ke topic ki– Pair of Linear Equations in Two Variables.
Iss article ka link me aapko yaha de raha hoon , iss article ko padhne ke liye iss blue link par click kijiye »»»
[What is polynomial and equation?].
I hope ki aap log iss article ko padhkar polynomials aur equations ke baare me acche se samajh gaye honge.
So friends, chaliye aage badhte hain...
Friends abb baat karte hain aaj ke topic ki– Pair of Linear Equations in Two Variables.
Friends jaisa ki iske naam se hi clear hai ki Pair of Linear Equations in Two Variables me do(two) linear equations hote hain jinme do(two) variables hote hain. Pair of Linear Equations in Two Variables iss general form me hote hain–
a1x + b1y + c1 = 0
a2x + b2y + c2 = 0
Jaha par a1 , b1 , c1 , a2 , b2 , c2 ye sabhi real numbers hain aur a12+b12≠0 ,
a22+b22≠0 ya phir short me kahein to a1≠0 , b1≠0 , a2≠0 , b2≠0.(c1 aur c2 zero ke equal ho sakte hain).
Example ke liye- 2x+3y–7=0
aur 9x–2y+8=0.
Chaliye ek aur example lete hain-
5x=y
aur –7x+2y=3.
Isi dekhne se aisa nahi lagta hai ki ye dono equations a1x + b1y + c1 = 0
a2x + b2y + c2 = 0form me hain. Lekin hum inhe rearrange karke iss form me likh sakte hain. Rearrange karne par inn dono equations ka form ye ho jaata hai-
5x+(–1)y+0=0
aur (–7)x+2y+(–3)=0
jo ki Pair of Linear Equations in Two Variables ke general form ke equivalent hai.
Ye to pata chal gaya aapko ki Pair of Linear Equations in Two Variables kya hota hai. Ab aap jaanta hain ki kisi bhi equation ka ek ya ek se zyada solutions jaroor hote hain(chahe wo solution real ho ya complex number ho).
[agar aap nahi jante hain ki real numbers aur complex numbers kise kehte hain to ye jaanne ke liye iss blue link par click kijiye »»»
What is complex number,real number,irrational number, rational number,integer,whole number,natural number?].
Aur uss equation ko solve karne ka method/tarikaa bhi jaroor hota hai. Mera ye sab bolne ka motive yahi tha jo aap sab abhi soch rahe ho. Aapke mind me abb ye question arise ho raha hoga ki Pair of Linear Equations in Two Variables ke kitne solution hote hai aur isse solve karne ka kya tarika/method hota hai? (Am I right?).
Chaliye abb baat karte hain Pair of Linear Equations in Two Variables ke solution ki aur hum kaise/kis method se Pair of Linear Equations in Two Variables ko solve kar sakte hain.
Friends, me aapko ye bata dena chahta hoon ki kisi Pair of Linear Equation in Two Variables ko solve karne ka matlab ye hota hai ki uss Pair of Linear Equation in Two Variables me jitne bhi variables hai unki value pata/find karna. Kisi Pair of Linear Equations in Two Variables ke solution ke liye teen(three) situations hoti hain:
1. One(unique) solution
2. Infinitely many solutions
3. No solution.
Matlab kisi Pair of Linear Equation in Two Variables ka ek(one) unique solution ho sakata hai. Ye bhi ho sakta hai ki kisi Pair of Linear Equation in Two Variables ke bohot saare(infinitely many) solutions ho. Aur ye bhi possible hai ki kisi Pair of Linear Equation in Two Variables ka koi solution naa ho(no solution).
Kisi bhi Pair of Linear Equation in Two Variables ko solve karne ke do(two) method hote hain–
1. Graphical(or Geometrical) method
2. Algebraic method
Ab algebraic method teen(three) tarah/type ke hote hain–
(a) Substitution method
(b) Elimination method
(c) Cross multiplication method
To agar ek tarah se dekha jaaye to basically Pair of Linear Equations in Two Variables ko solve karne ke chaar(four) methods hote hain–
1. Graphical(or Geometrical) method
2. Substitution method
3. Elimination method
4. Cross multiplication method
Iss article me aapko sirf inn chaaro me se first method yaani Graphical(or Geometrical) method ke baare me bataoonga.
To aaeeye jaante hain Graphical(or Geometrical) method ke baare mein...
Graphical(or Geometrical) method
Iss method ko graphical method isliye kehte hai kyuki isme Pair of Linear Equations in Two Variables me jo dono linear equations (in two variable) hote hain , unka graph draw karna padta hai.
Kisi bhi Pair of Linear Equations in Two Variables ko graphical method se solve karne ke liye uss Pair of Linear Equation in Two Variables me jo dono linear equation (in two variables) hote hain unn dono ke graph ek hi Cartesian plane(graph paper) par draw kar liya jaata hai.[Inn dono ka graph ek straight line hota hai aur isi wajah se inhe linear kaha jaata hai; linear equation ka matlab hota hai– aisa equation jiska graph ek straight line ho]. Aur jiss point par dono linear equation (in two variables) ke graph ek doosre ko intersect karte hain ; uss point ki values/coordinates hi uss Pair of Linear Equation in Two Variables ka solution(one unique solution) hoti hain. Agar dono ke graph kisi bhi point par intersect naa karein to uss Pair of Linear Equation in Two Variables ka koi solution nahi hoga(no solution). Agar dono ke graph ek doosre ko sabhi point par intersect karein to uss Pair of Linear Equation in Two Variables ke bohot saare solution honge(infinitely many solutions).
To chaliye iss method se Pair of Linear Equations in Two Variables se related kuch problems ko solve karte hain...
Ex.1. Solve the Pair of Linear Equation in Two Variables x+2y=4 and 3x–y=5 using graphical method.
Solution:- Iss Pair of Linear Equation in Two Variables ko solve karne ke liye sabse pehle hame x+2y=4 ka graph draw karna hoga aur phir ussi Cartesian plane(graph paper) par
3x–y=5 ka graph draw karna hoga. To start karte hain x+2y=4 ka graph draw karna se. Iska graph draw karne ke liye iss equation ko y ke form me likhna hoga. y ke form me likhne par ye equation iss tarah ka ho jaayega-
y=4-x
2
Ab isme apni taraf se x ki kuch values rakhte hai. Hum x ki value koi bhi real number rakh sakte hain but hame x ki values wahi rakhni chahiye jo small aur simple number ho. Kam se kam 4 ya 5 values, x ki ,apni taraf se rakh lijiye. Aur phir usse unke respective y ki 4 ya 5 values bhi aapko milengi. Jaise ki iss table ko dekhiye–
Isme maine apni taraf se x ki 5 values-
–4, –2, 0, 2 aur 4 li hai. Phir har(each) x ki value ke liye y ki ek value likaali. Aur y ki value ko table me uski x ki value ke neeche rakh diya. Ab isse hame har(each) x aur y ki value se ek point milta hai. Yaha par hame 5 points milte hain: (–4,4), (–2,3), (0,2), (2,1) aur (4,0).
Ab inn paancho points ko ek graph paper par plot karte hain aujr phir inn paancho points ko ek straight line se mila dete hain. Iss tarah se equation x+2y=4 ka graph draw ho jaata hai.
Ab hame equation 3x–y=5 ka graph draw karna hai. Iske liye hame iske saath bhi wahi sab karna hoga jo hamne pehle equation ke saath kiya. Ye sab karne ke baad iska bhi graph draw ho jaayega. Iska graph bhi ussi graph paper par draw karna hai jis par hamne pehle waale equation ka graph draw kiya tha. Dono equations ka graph draw karne ke baad wo aapko kuch iss tarah ka dikhega-
Dono equations x+2y=4 and 3x–y=5 ke graph ek doosre ko point (2,1) par intersect kar rahe hain. So, Pair of Linear Equation in Two Variables x+2y=4 and 3x–y=5 ka solution (2,1) hai jisme x=2 aur y=1 hai.
(Exactly one/unique solution)
(Intersecting lines)
Ex.2. Solve the Pair of Linear Equation in Two Variables 6x–3y=12 and y=2x–4 using graphical method.
Solution:- Iss Pair of Linear Equation in Two Variables ko solve karne ke liye same wahi procedure follow karna hoga jaisa ki Ex.1. me kiya gaya hai. Ye sab kuch karne ke baad inn equations 6x–3y=12 and y=2x–4 ka graph kuch iss tarah se banega-
Solution:- Iss Pair of Linear Equation in Two Variables ko solve karne ke liye bhi same to same waisa hi karenge jaisa ki upar bataye gaye dono examples me kiya gaya hai. Phir iss tarah inn dono equations 3x–2y=2 and 3x–2y= –2 ka graph draw ho jaayega. Graph draw hone ke baad wo aapko kuch iss tarah ka dikhega–
(Parallel lines).
Ab zara iss situation par vichaar kijiye. Maan lijiye ki aap ek Pair of Linear Equation in Two Variables ko graphical method se solve kar rahe hai. Aisa karne ke liye aapne sabse pehle kisi dono me se kisi ek equation ko y ke form me likha , phir apni taraf se x ki kuch vakues rakhi aisa karne ke baad aapko sabi x ki values ke corresponding y ki values bhi mil gayi. Aapne sabhi points ko graph paper par plot bhi kar diya. Ab usse aapko iss equation ka graph mil gaya. Ab doosre bache hue equation ka graph draw karne ke liye bhi aapne phir se yahi sab kiya jo pehle equation ka graph draw karne ke liye kiya tha. Dono equations ka graph draw Karne ke baad aapko ye dekhne ko milta hai ki dono equations ke graph parallel straight lines hai matlab aapko ye pata chalta hai ki uss Pair of Linear Equation in Two Variables ka koi solution hai hi nahi. To bataiye aapko kaisa lagega. Aapki ssari mehnat aur uss problem ko solve karne me laga time barbaad/waste ho jaayegi.
To yaha par aapke mind me ye question hit hona chahiye ki kya koi aisa tarikaa/way/method nahi hai jisse hum ye dekhte hi bata de ki kisi Pair of Linear Equation in Two Variables ka solution hai bhi ki nahi.
Iska sawaal ka jawaab hai haa! Aisa ek method hai jisse hum ye dekhte hi bata de ki kisi Pair of Linear Equation in Two Variables ka solution hai bhi ki nahi. Aur sirf ye hi nahi, iss method ke prayog(use) se hum ye bhi bata saktae hain ki kisi Pair of Linear Equation in Two Variables ka ek(one) unique solution hai ya infinitely many solutions.
Ab chaliye dekhte hain ki ye method kya hai aur ise kaise use karte hain.
Sabse pehle hum diye gaye Pair of Linear Equation in Two Variables me a1/a2 aur b1/b2 nikaal lete hain. Agar ye dono equal nahi hai to uss Pair of Linear Equation in Two Variables ka graph intersecting lines hoga aur iss tarah iss situation me sirf ek(one) unique solution hoga. Agar a1/a2 aur b1/b2 equal hain to hum c1/c2 nikaalte hain. Agar c1/c2 , a1/a2 aur b1/b2 ke equal hai to uss Pair of Linear Equation in Two Variables ka graph coincident lines hoga aur iss tarah iss situation me infinitely many solutions honge. Aur agar c1/c2 , a1/a2 aur b1/b2 ke equal nahi hai to uss Pair of Linear Equation in Two Variables ka graph parallel lines hoga aur iss tarah iss situation me koi solution nahi hoga.
Iss table ko dekhkar aap iss method ko acche se samajh jaayenge-
Aapne is article ko padhkar kya seekha?
CHECK YOUR KNOWLEDGE
Give answers:
Q.1-Is the Pair of Linear Equations in Two Variables 5x-4+8=0 and 7x+6y–9=0 consistent?
Q.2-Which type of graph has the Pair of Linear Equations in Two Variables 9x+3y+12=0 and 18x+6y+24=0 ; intersecting lines, coincident lines or parallel lines?
Q.3-Solve the Pair of Linear Equations in Two Variables 6x–3y+10=0 and 2x–y+9=0 by substitution method?
Aap apne answers hame comment ke through bata sakte hain.
THANKS FOR READING THIS BLOG.
a2x + b2y + c2 = 0
Jaha par a1 , b1 , c1 , a2 , b2 , c2 ye sabhi real numbers hain aur a12+b12≠0 ,
a22+b22≠0 ya phir short me kahein to a1≠0 , b1≠0 , a2≠0 , b2≠0.(c1 aur c2 zero ke equal ho sakte hain).
Example ke liye- 2x+3y–7=0
aur 9x–2y+8=0.
Chaliye ek aur example lete hain-
5x=y
aur –7x+2y=3.
Isi dekhne se aisa nahi lagta hai ki ye dono equations a1x + b1y + c1 = 0
a2x + b2y + c2 = 0form me hain. Lekin hum inhe rearrange karke iss form me likh sakte hain. Rearrange karne par inn dono equations ka form ye ho jaata hai-
5x+(–1)y+0=0
aur (–7)x+2y+(–3)=0
jo ki Pair of Linear Equations in Two Variables ke general form ke equivalent hai.
Ye to pata chal gaya aapko ki Pair of Linear Equations in Two Variables kya hota hai. Ab aap jaanta hain ki kisi bhi equation ka ek ya ek se zyada solutions jaroor hote hain(chahe wo solution real ho ya complex number ho).
[agar aap nahi jante hain ki real numbers aur complex numbers kise kehte hain to ye jaanne ke liye iss blue link par click kijiye »»»
What is complex number,real number,irrational number, rational number,integer,whole number,natural number?].
Aur uss equation ko solve karne ka method/tarikaa bhi jaroor hota hai. Mera ye sab bolne ka motive yahi tha jo aap sab abhi soch rahe ho. Aapke mind me abb ye question arise ho raha hoga ki Pair of Linear Equations in Two Variables ke kitne solution hote hai aur isse solve karne ka kya tarika/method hota hai? (Am I right?).
Chaliye abb baat karte hain Pair of Linear Equations in Two Variables ke solution ki aur hum kaise/kis method se Pair of Linear Equations in Two Variables ko solve kar sakte hain.
Friends, me aapko ye bata dena chahta hoon ki kisi Pair of Linear Equation in Two Variables ko solve karne ka matlab ye hota hai ki uss Pair of Linear Equation in Two Variables me jitne bhi variables hai unki value pata/find karna. Kisi Pair of Linear Equations in Two Variables ke solution ke liye teen(three) situations hoti hain:
1. One(unique) solution
2. Infinitely many solutions
3. No solution.
Matlab kisi Pair of Linear Equation in Two Variables ka ek(one) unique solution ho sakata hai. Ye bhi ho sakta hai ki kisi Pair of Linear Equation in Two Variables ke bohot saare(infinitely many) solutions ho. Aur ye bhi possible hai ki kisi Pair of Linear Equation in Two Variables ka koi solution naa ho(no solution).
Kisi bhi Pair of Linear Equation in Two Variables ko solve karne ke do(two) method hote hain–
1. Graphical(or Geometrical) method
2. Algebraic method
Ab algebraic method teen(three) tarah/type ke hote hain–
(a) Substitution method
(b) Elimination method
(c) Cross multiplication method
To agar ek tarah se dekha jaaye to basically Pair of Linear Equations in Two Variables ko solve karne ke chaar(four) methods hote hain–
1. Graphical(or Geometrical) method
2. Substitution method
3. Elimination method
4. Cross multiplication method
Iss article me aapko sirf inn chaaro me se first method yaani Graphical(or Geometrical) method ke baare me bataoonga.
To aaeeye jaante hain Graphical(or Geometrical) method ke baare mein...
Graphical(or Geometrical) method
Iss method ko graphical method isliye kehte hai kyuki isme Pair of Linear Equations in Two Variables me jo dono linear equations (in two variable) hote hain , unka graph draw karna padta hai.
Kisi bhi Pair of Linear Equations in Two Variables ko graphical method se solve karne ke liye uss Pair of Linear Equation in Two Variables me jo dono linear equation (in two variables) hote hain unn dono ke graph ek hi Cartesian plane(graph paper) par draw kar liya jaata hai.[Inn dono ka graph ek straight line hota hai aur isi wajah se inhe linear kaha jaata hai; linear equation ka matlab hota hai– aisa equation jiska graph ek straight line ho]. Aur jiss point par dono linear equation (in two variables) ke graph ek doosre ko intersect karte hain ; uss point ki values/coordinates hi uss Pair of Linear Equation in Two Variables ka solution(one unique solution) hoti hain. Agar dono ke graph kisi bhi point par intersect naa karein to uss Pair of Linear Equation in Two Variables ka koi solution nahi hoga(no solution). Agar dono ke graph ek doosre ko sabhi point par intersect karein to uss Pair of Linear Equation in Two Variables ke bohot saare solution honge(infinitely many solutions).
To chaliye iss method se Pair of Linear Equations in Two Variables se related kuch problems ko solve karte hain...
Ex.1. Solve the Pair of Linear Equation in Two Variables x+2y=4 and 3x–y=5 using graphical method.
Solution:- Iss Pair of Linear Equation in Two Variables ko solve karne ke liye sabse pehle hame x+2y=4 ka graph draw karna hoga aur phir ussi Cartesian plane(graph paper) par
3x–y=5 ka graph draw karna hoga. To start karte hain x+2y=4 ka graph draw karna se. Iska graph draw karne ke liye iss equation ko y ke form me likhna hoga. y ke form me likhne par ye equation iss tarah ka ho jaayega-
y=4-x
2
Ab isme apni taraf se x ki kuch values rakhte hai. Hum x ki value koi bhi real number rakh sakte hain but hame x ki values wahi rakhni chahiye jo small aur simple number ho. Kam se kam 4 ya 5 values, x ki ,apni taraf se rakh lijiye. Aur phir usse unke respective y ki 4 ya 5 values bhi aapko milengi. Jaise ki iss table ko dekhiye–
Isme maine apni taraf se x ki 5 values-
–4, –2, 0, 2 aur 4 li hai. Phir har(each) x ki value ke liye y ki ek value likaali. Aur y ki value ko table me uski x ki value ke neeche rakh diya. Ab isse hame har(each) x aur y ki value se ek point milta hai. Yaha par hame 5 points milte hain: (–4,4), (–2,3), (0,2), (2,1) aur (4,0).
Ab inn paancho points ko ek graph paper par plot karte hain aujr phir inn paancho points ko ek straight line se mila dete hain. Iss tarah se equation x+2y=4 ka graph draw ho jaata hai.
Ab hame equation 3x–y=5 ka graph draw karna hai. Iske liye hame iske saath bhi wahi sab karna hoga jo hamne pehle equation ke saath kiya. Ye sab karne ke baad iska bhi graph draw ho jaayega. Iska graph bhi ussi graph paper par draw karna hai jis par hamne pehle waale equation ka graph draw kiya tha. Dono equations ka graph draw karne ke baad wo aapko kuch iss tarah ka dikhega-
Dono equations x+2y=4 and 3x–y=5 ke graph ek doosre ko point (2,1) par intersect kar rahe hain. So, Pair of Linear Equation in Two Variables x+2y=4 and 3x–y=5 ka solution (2,1) hai jisme x=2 aur y=1 hai.
(Exactly one/unique solution)
(Intersecting lines)
Ex.2. Solve the Pair of Linear Equation in Two Variables 6x–3y=12 and y=2x–4 using graphical method.
Solution:- Iss Pair of Linear Equation in Two Variables ko solve karne ke liye same wahi procedure follow karna hoga jaisa ki Ex.1. me kiya gaya hai. Ye sab kuch karne ke baad inn equations 6x–3y=12 and y=2x–4 ka graph kuch iss tarah se banega-
Dono equations ke graph ek doosre ko poori tarah se cover kar rahe hain. Inn dono equations ke graph coincident lines hain. Inn dono equations ka graph ek hi straight line hain ya phir ye bhi keh sakte hain ki inn dono equations ke graph ek doosre ko har(every) point par intersect kar rahe hain. So, iss line par aane waale saare points ,Pair of Linear Equation in Two Variables 6x–3y=12 and y=2x–4 ke solutions hain. Jaise ki (0,–4), (2,0), (1,–2) etc. inke solutions hain. Ye sabhi points inke graph par aate hain.
x= 0, 2, 1, ...
y= –4, 2, –2, ... etc. iske solutions hain.
(Infinitely many solutions)
(Coincident lines)
Ex.3. Solve the Pair of Linear Equation in Two Variables 3x–2y=2 and 3x–2y= –2 using graphical method.
Solution:- Iss Pair of Linear Equation in Two Variables ko solve karne ke liye bhi same to same waisa hi karenge jaisa ki upar bataye gaye dono examples me kiya gaya hai. Phir iss tarah inn dono equations 3x–2y=2 and 3x–2y= –2 ka graph draw ho jaayega. Graph draw hone ke baad wo aapko kuch iss tarah ka dikhega–
Inke graph ko dekhne se ya pata chal raha hai ki inn dono equations 3x–2y=2 and 3x–2y= –2 ke graph ek doosre ko kahi par bhi nahi intersect kar rahe hai aur naa hi inn lines ko aagae badhaane par kabhi intersect karenge. Ye dono lines parallel hain. So, iss Pair of Linear Equation in Two Variable
3x–2y=2 and 3x–2y=–2 ka koi solution nahi hai.
(No solution)(Parallel lines).
Ab zara iss situation par vichaar kijiye. Maan lijiye ki aap ek Pair of Linear Equation in Two Variables ko graphical method se solve kar rahe hai. Aisa karne ke liye aapne sabse pehle kisi dono me se kisi ek equation ko y ke form me likha , phir apni taraf se x ki kuch vakues rakhi aisa karne ke baad aapko sabi x ki values ke corresponding y ki values bhi mil gayi. Aapne sabhi points ko graph paper par plot bhi kar diya. Ab usse aapko iss equation ka graph mil gaya. Ab doosre bache hue equation ka graph draw karne ke liye bhi aapne phir se yahi sab kiya jo pehle equation ka graph draw karne ke liye kiya tha. Dono equations ka graph draw Karne ke baad aapko ye dekhne ko milta hai ki dono equations ke graph parallel straight lines hai matlab aapko ye pata chalta hai ki uss Pair of Linear Equation in Two Variables ka koi solution hai hi nahi. To bataiye aapko kaisa lagega. Aapki ssari mehnat aur uss problem ko solve karne me laga time barbaad/waste ho jaayegi.
To yaha par aapke mind me ye question hit hona chahiye ki kya koi aisa tarikaa/way/method nahi hai jisse hum ye dekhte hi bata de ki kisi Pair of Linear Equation in Two Variables ka solution hai bhi ki nahi.
Iska sawaal ka jawaab hai haa! Aisa ek method hai jisse hum ye dekhte hi bata de ki kisi Pair of Linear Equation in Two Variables ka solution hai bhi ki nahi. Aur sirf ye hi nahi, iss method ke prayog(use) se hum ye bhi bata saktae hain ki kisi Pair of Linear Equation in Two Variables ka ek(one) unique solution hai ya infinitely many solutions.
Ab chaliye dekhte hain ki ye method kya hai aur ise kaise use karte hain.
Sabse pehle hum diye gaye Pair of Linear Equation in Two Variables me a1/a2 aur b1/b2 nikaal lete hain. Agar ye dono equal nahi hai to uss Pair of Linear Equation in Two Variables ka graph intersecting lines hoga aur iss tarah iss situation me sirf ek(one) unique solution hoga. Agar a1/a2 aur b1/b2 equal hain to hum c1/c2 nikaalte hain. Agar c1/c2 , a1/a2 aur b1/b2 ke equal hai to uss Pair of Linear Equation in Two Variables ka graph coincident lines hoga aur iss tarah iss situation me infinitely many solutions honge. Aur agar c1/c2 , a1/a2 aur b1/b2 ke equal nahi hai to uss Pair of Linear Equation in Two Variables ka graph parallel lines hoga aur iss tarah iss situation me koi solution nahi hoga.
Iss table ko dekhkar aap iss method ko acche se samajh jaayenge-
[Note:- Jin Pair of Linear Equations in Two Variables ka solution hota hai chahe wo ek ho ya infinitely many, unhe consistent kehte hai aur jin Pair of Linear Equations in Two Variables ka koi bhi solution nahi hota usse inconsistent kehte hain].
I hope ki aapko mera ye article pasand aaya hoga aur mujhe ummeed hai ki aapko Pair of Linear Equations in Two Variables ke baare me kafi jaankari mili hogi. Maine aapko aasaan sabdo me Pair of Linear Equations in Two Variables ke baare me samjhaane ki koshish ki hai.
I hope ki aapko sab kuch acche se samajh me aa gaya hoga.Aur agar aapko koi cheez samajh me nahi aayi ho to commemt ke through aap hame bata sakte hain. Agar aapko ye post accha laga ho to comment ke maadhyam se aap hame support kar sakte hai.Aapne is article ko padhkar kya seekha?
CHECK YOUR KNOWLEDGE
Give answers:
Q.1-Is the Pair of Linear Equations in Two Variables 5x-4+8=0 and 7x+6y–9=0 consistent?
Q.2-Which type of graph has the Pair of Linear Equations in Two Variables 9x+3y+12=0 and 18x+6y+24=0 ; intersecting lines, coincident lines or parallel lines?
Q.3-Solve the Pair of Linear Equations in Two Variables 6x–3y+10=0 and 2x–y+9=0 by substitution method?
Aap apne answers hame comment ke through bata sakte hain.
THANKS FOR READING THIS BLOG.
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