NCERT Class X Chapter 3: Pair of Linear Equations In Two Variables Exercise 3.3 Question 1(ii)

NCERT Class X Chapter 3: Pair of Linear Equations In Two Variables Exercise 3.3 Question 1(ii)

Question:

Solve the following pair of linear equations by the elimination method and the substitution method: 3x + 4y = 10 and 2x – 2y = 2

Given:

3x + 4y = 10
2x – 2y = 2

To Find:

The values of x and y using elimination and substitution methods.

Formula:

No specific formula, but the elimination and substitution methods are used.

Solution:

Elimination Method:

1. Multiply the second equation by 2 to make the coefficients of y opposites: 4x - 4y = 4

2. Add the first equation and the modified second equation: (3x + 4y) + (4x - 4y) = 10 + 4 ⇒ 7x = 14 ⇒ x = 2

3. Substitute x = 2 into either original equation to solve for y. Using the second equation: 2(2) - 2y = 2 ⇒ 4 - 2y = 2 ⇒ 2y = 2 ⇒ y = 1

Substitution Method:

1. Solve the second equation for x: 2x - 2y = 2 ⇒ 2x = 2y + 2 ⇒ x = y + 1

2. Substitute this expression for x into the first equation: 3(y + 1) + 4y = 10 ⇒ 3y + 3 + 4y = 10 ⇒ 7y = 7 ⇒ y = 1

3. Substitute y = 1 back into either original equation or the expression for x. Using x = y + 1: x = 1 + 1 ⇒ x = 2

Result:

x = 2, y = 1
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