Solve the following pair of equations using substitution method:
$\frac{5 y}{2} - \frac{x}{3} = 8$
$\frac{y}{2} + \frac{5 x}{3} = 12$

x = 2; y = 7

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x = 6; y = 4

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x = 7; y = 1

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x = 8; y = 3

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Solution

The correct option is B $x = 6; y = 4$
$\frac{5 y}{2} - \frac{x}{3} = 8 . . . (1) \frac{y}{2} + \frac{5 x}{3} = 12 . . . (2)$

Let $\frac{y}{2} = a$ and $\frac{x}{3} = b$
So, the original equations reduce to
$5 a - b = 8$ ... $(1)$
$a + 5 b = 12$ ... $(2)$
From $(1), b = 5 a - 8$

Substituting $b = 5 a - 8$ in $(2)$ , we get
$a + 5 (5 a - 8) = 12$
$a + 25 a - 40 = 12$
$26 a = 52$
$a = 2$

So, $b = 5 a - 8$
$b = 10 - 8 = 2$

But $\frac{y}{2} = a$ or $y = 2 a = 4$
$\frac{x}{3} = b$ or $x = 3 b = 6$

$x = 6, y = 4$
Option $B$ .

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