Question

3(y + 5) = x\\
\frac{x}{y} = 2\\
if (x, y) is the solution to the system of equations above, what is the value of y?\\
a) -3\\
b) -9\\
c) -12\\
d) -15

Explanation:

Step1: Express x from second equation

From $\frac{x}{y}=2$, multiply both sides by $y$:
$x=2y$

Step2: Substitute x into first equation

Replace $x$ in $3(y+5)=x$ with $2y$:
$3(y+5)=2y$

Step3: Expand left side of equation

Distribute the 3:
$3y+15=2y$

Step4: Solve for y

Subtract $2y$ and 15 from both sides:
$3y-2y=-15$
$y=-15$

Answer:

D) $-15$