Question

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

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

Answer 1

The correct option is B

$x=\frac{94}{57},y=\frac{51}{19}$

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

Multiply by 6 on both sides

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

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

Multiply by 6 on both sides

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

(1) ⇒ $x=\frac{10y-12}{9}$............(3)

Substituting equation (3) in equation (2)

3[$\frac{10y-12}{9}$] + 3y = 13

10y - 12 + 9y = 39

19y = 51

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

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