Question

On solving $\frac{2}{3}x+5y=12,x+\frac{3}{2}y=6,$ we get:
(a) x = 3, y = 2
(b) x = 6, y = 1
(c) x = −3, y = −2
(d) x = 6, y = 2

Answer 1

The correct option is (a).

$\frac{2}{3}x+5y=12$
2x + 15y = 36 ....(i)
$x+\frac{3}{2}y=6$
2x + 3y = 12 ....(ii)
On subtracting (ii) from (i), we get:
12y = (36 − 12) = 24 ⇒ y = 2
On substituting y = 2 in (i), we get:
2x + 30 = 36 ⇒ 2x = (36 − 30) = 6 ⇒ x = 3
∴​ x = 3 and y = 2