Question

Solve and find value of y.

$\frac{3x}{2}-\frac{5y}{3}=-2$ ; $\frac{x}{2}+\frac{y}{2}=\frac{13}{6}$

• A. $y=\frac{117}{54}$
• B. $y=\frac{51}{19}$
• C. $y=\frac{57}{19}$
• D. $y=\frac{94}{57}$

Answer 1

The correct option is B

$y=\frac{51}{19}$

$\frac{3x}{2}$ - $\frac{5y}{3}$ = -2

LCM of 2 and 3 is 6. Multiply by 6 on both sides

$9x-10y=-12$ -------------(1)

$\frac{x}{2}+\frac{y}{2}=\frac{13}{6}$

LCM is 6. Multiply by 6 on both sides

$3x+3y=13$ --------------(2)

Multiply equation (2) by 3 to eliminate x ; so we get,

$9x+9y=39$...............(3)

Subtract (3) from (1) we have

$-19y=-51\Rightarrow y=\frac{51}{19}$

Substitute this in one of the equation and we get

$x=10\left[\frac{\frac{51}{19}-12}{9}\right]=\frac{282}{19\times 9}=\frac{94}{3\times 19}=\frac{94}{57}$

$\Rightarrow x=\frac{94}{57}$