Q118
ArithmeticAlgebra, Equations & Operations
$2x - 3y = -12$ and $\frac{x}{y} = \frac{3}{4}$, what is the value of $x$ and $y$?
- a.$x = 6$, $y = 9$
- b.$x = 6$, $y = 8$
- c.$x = 4$, $y = 3$
- d.$x = 8$, $y = 4$
Answer: (B) $x = 6$, $y = 8$
From $\frac{x}{y} = \frac{3}{4}$, $x = \frac{3y}{4}$. Substituting in $2x - 3y = -12$: $\frac{3y}{2} - 3y = -12$, so $-\frac{3y}{2} = -12$, giving $y = 8$ and $x = 6$. The quickest exam method is to test the options: only $x = 6$, $y = 8$ satisfies both conditions ($12 - 24 = -12$ and $\frac{6}{8} = \frac{3}{4}$). Option A fails the ratio ($\frac{6}{9} = \frac{2}{3}$), and options C and D give a ratio greater than 1.