Solve the following pair of linear equations by the elimination method and the substitution method

3x – 5y – 4 = 0 and 9x = 2y + 7

#### Solution

3x – 5y – 4 = 0 and 9x = 2y + 7

By elimination method

3x – 5y – 4 = 0

3x – 5y = 4 ...(i)

9x = 2y + 7

9x – 2y = 7 ... (ii)

Multiplying equation (i) by 3, we get

9 x – 15 y = 11 ... (iii)

9x – 2y = 7 ... (ii)

Subtracting equation (ii) from equation (iii), we get

-13y = 5

y = -5/13

Putting value in equation (i), we get

3x – 5y = 4 ... (i)

3x - 5(-5/13) = 4

Multiplying by 13 we get

39x + 25 = 52

39x = 27

x =27/39 = 9/13

Hence our answer is x = 9/13 and y = - 5/13

By substitution method

3x – 5y = 4 ... (i)

Adding 5y both side we get

3x = 4 + 5y

Dividing by 3 we get

x = (4 + 5y )/3 ... (iv)

Putting this value in equation (ii) we get

9x – 2y = 7 ... (ii)

9 ((4 + 5y )/3) – 2y = 7

Solve it we get

3(4 + 5y ) – 2y = 7

12 + 15y – 2y = 7

13y = - 5

y = -5/13

x = `(4+5xx(-5/13))/3`

=`(4-25/13)/3 = ((4xx13-25)/13)/3`

= `27/(13xx3)= 27/39=9/3`

Hence we get x = 9/13 and y = - 5/13 again.