Question

Solve the following pair of linear equation by the elimination method and the substitution method: 

3x + 4y = 10 and 2x – 2y = 2

Answer 1

3x + 4y = 10 and 2x – 2y = 2

By elimination method

3x + 4y = 10          ...(1)

2x – 2y = 2            ...(2)

Multiplying equation (ii) by 2, we get

4x – 4y = 4            ...(3)

3x + 4y = 10             

Adding equation (1) and (3), we get

7x + 0 = 14

Dividing both side by 7, we get

x = `14/7`

x = 2

Putting in equation (1), we get

3x + 4y = 10

3(2) + 4y = 10

6 + 4y = 10

4y = 10 – 6

4y = 4

y = `4/4`

y = 1

Hence, answer is x = 2, y = 1

By substitution method

3x + 4y = 10 

y = `(10-3x)/4`     

2x - 2y = 10

x - y = 1

Putting y = `(10 - 3x)/4` in (2) we get

⇒ `x - (10 - 3x)/4 = 1`

⇒ 4x - 10 + 3x = 4

⇒ 7x = 14

⇒ `x = 14/7`

⇒ x = 2

Putting x = 2 in (1), we get

y = `(10 - 3 xx2)/4`

y = `(10 - 6)/4`

y = `4/4`

y = 1

Hence, x = 2 and y = 1