full-page ad: \( \$ 125 \) 9. What is the \( y \)-coordinate of the solution to the system of equations shown? \( \left\{\begin{array}{l}2 x+3 y=5 \\ 3 x-2 y=-12 \\ \begin{array}{ll}\text { (A) }-3 & \text { (C) } 2 \\ \text { (B) }-2 & \text { (D) } 3\end{array}\end{array}\right. \)

To solve the system of equations \(2x + 3y = 5\) and \(3x - 2y = -12\), we can use either the substitution or elimination method. First, let's express one variable in terms of the other using the first equation. Rearranging gives us: \[3y = 5 - 2x \quad \Rightarrow \quad y = \frac{5 - 2x}{3}.\] Next, substitute \(y\) into the second equation: \[3x - 2\left(\frac{5 - 2x}{3}\right) = -12.\] Clear the fraction by multiplying everything by 3: \[9x - 2(5 - 2x) = -36.\] This simplifies to: \[9x - 10 + 4x = -36 \quad \Rightarrow \quad 13x - 10 = -36 \quad \Rightarrow \quad 13x = -26 \quad \Rightarrow \quad x = -2.\] Now, substitute \(x = -2\) back into the first equation to find \(y\): \[2(-2) + 3y = 5 \quad \Rightarrow \quad -4 + 3y = 5 \quad \Rightarrow \quad 3y = 9 \quad \Rightarrow \quad y = 3.\] Thus, the \(y\)-coordinate of the solution to the system of equations is \(3\). The answer is (D) \(3\).