Class 10 Maths: Pair of Linear Equations ko Elimination Method se kaise solve karein

Pair of linear equations mein do equations hoti hain aur humein dono ko satisfy karne wale x aur y ke values nikalne hote hain. Elimination method ka idea simple hai: kisi ek variable ko add ya subtract karke hata do, phir bache hue variable ko solve karo.

Elimination method ka basic idea

Maan lijiye:

2x + 3y = 13   ...(1)
2x - y = 5     ...(2)

Dono equations mein 2x same hai. Equation (2) ko equation (1) se subtract karne par x eliminate ho jayega:

(2x + 3y) - (2x - y) = 13 - 5
4y = 8
y = 2

Ab y = 2 ko equation (2) mein put kijiye:

2x - 2 = 5
2x = 7
x = 7/2

Isliye solution hai:

x = 7/2, y = 2

Jab coefficients same na hon

Ab dekhiye:

3x + 2y = 16   ...(1)
2x + 3y = 19   ...(2)

Yahan kisi coefficient ko equal karne ke liye equation (1) ko 2 se aur equation (2) ko 3 se multiply karte hain:

6x + 4y = 32   ...(3)
6x + 9y = 57   ...(4)

Equation (4) se equation (3) subtract karein:

5y = 25
y = 5

Equation (2) mein y = 5 rakhein:

2x + 15 = 19
2x = 4
x = 2

Solution (x, y) = (2, 5) hai.

Answer check kaise karein

Answer ko dono original equations mein put kijiye. Agar x = 2 aur y = 5 ko equation (1) mein rakhein:

3(2) + 2(5) = 6 + 10 = 16

Equation (2) mein:

2(2) + 3(5) = 4 + 15 = 19

Dono answers match karte hain, isliye solution verify ho gaya.

Common mistakes

1. Puri equation ko multiply karne ki jagah sirf ek term ko multiply karna. 2. Minus sign ko bracket ke andar distribute na karna. 3. Variable eliminate karne ke baad constant side par arithmetic mistake karna. 4. Final values ko original equations mein check na karna.

Practice question

Elimination method se solve kijiye:

4x + 3y = 23
2x - 3y = 1

Hint: Dono equations ko add karke y eliminate ho jayega. Answer check karna mat bhoolna.

Quick recap

Elimination method ke steps hain: coefficients ko suitable multiplication se equal karo, equations ko add/subtract karke ek variable hatao, bache variable ko solve karo, aur final pair ko dono equations mein verify karo.

Apna question ya attempt DoubtPay AI ke study space mein bhejkar step-by-step explanation, hint ya answer check le sakte hain. AI answer ko apni textbook ya teacher ke method se verify karna hamesha achha habit hai.

FAQs

Elimination method kab use karna chahiye?

Jab kisi variable ke coefficients equal ya easily equal kiye ja sakte hon, tab elimination method fast hota hai.

Kya answer decimal mein likh sakte hain?

Haan, lekin exam mein exact fraction form aksar zyada clear hoti hai. Question ke instructions follow karein.

Agar dono variables eliminate ho jayen to?

Equations dependent ya inconsistent ho sakti hain. Aise case mein class notes ke consistency rules ke saath result interpret karein.