Question

3
2x - 3y = -12
x + y = 9

Explanation:

Step1: Solve the second equation for x

From \( x + y = 9 \), we can express \( x \) as \( x = 9 - y \).

Step2: Substitute x into the first equation

Substitute \( x = 9 - y \) into \( 2x - 3y = -12 \):
\[

$$\begin{align*} 2(9 - y) - 3y &= -12\\ 18 - 2y - 3y &= -12\\ 18 - 5y &= -12 \end{align*}$$

\]

Step3: Solve for y

Subtract 18 from both sides:
\[
-5y = -12 - 18\\
-5y = -30
\]
Divide both sides by -5:
\[
y = \frac{-30}{-5} = 6
\]

Step4: Solve for x

Substitute \( y = 6 \) into \( x = 9 - y \):
\[
x = 9 - 6 = 3
\]

Answer:

\( x = 3 \), \( y = 6 \)