Question

Solve each of the following systems of simultaneous linear equations by the method of substitution

(i) 4x – 5y = 39, 2x – 7y = 51

(ii) 5x – 2y = 19, 3x + y = 18

Answer 1

(i) 4x – 5y = 39, 2x – 7y = 51

The given equations are

4x – 5y = 39 …(i)

and 2x – 7y = 51 …(ii)

From equation (ii),

2x – 51 = 7y

Hence the required solution is x = 1, y = -7.

(ii) 5x – 2y = 19, 3x + y = 18

The given equations are

5x – 2y = 19 …(i)

and 3x + y = 18 …(ii)

From (ii), y = 18 – 3x …(iii)

Substituting y from (iii) in (i), we get

5x – 2(18 – 3x) = 19

⇒ 5x – 36 + 6x = 19

⇒ 11x = 55

⇒ x = 5

Putting x = 5 in (iii), we get

y = 18 – 3 × 5

y = 18 – 15 = 3

Hence the required solution is x = 5 and y = 3.