Question

`8/x + 5y = 11 and 4/x + 3y = 7` have solution ______.

Options

• `(1/2, -1)`

• (2, −3)

• `(1/4, -3)`

• (−2, 3)

Answer 1

`8/x + 5y = 11 and 4/x + 3y = 7` have solution (−2, 3).

Explanation:

Let us assume: `1/x = a`

Equations become:

8a + 5y = 11     ...(i)

4a + 3y = 7      ...(ii)

Multiplying equation (ii) by 2:

2(4a + 3y) = 2(7)

8a + 6y = 14     ...(iii)

Subtracting equation (i) from equation (iii):

(8a + 6y) − (8a + 5y) = 14 − 11

8a + 6y − 8a − 5y = 3

6y − 5y = 3

∴ y = 3

Substitute y = 3 in equation (ii):

4a + 3 × 3 = 7

4a + 9 = 7

4a = −2

a = `4/-2`

∴ a = −2

Now, substitute a = −2 in `1/x = a`,

`1/x = -2`

`x = (-2)/1`

∴ x = −2

Hence, x = −2 and y = 3.