Question

solve the system of equations.

• 2x + 15y = -24

2x + 9y = 24
x =

y =

Explanation:

Step1: Add the two equations

To eliminate \( x \), we add the two given equations:
\[

$$\begin{align*} (-2x + 15y) + (2x + 9y) &= -24 + 24\\ -2x + 15y + 2x + 9y &= 0\\ 24y &= 0 \end{align*}$$

\]

Step2: Solve for \( y \)

Divide both sides of \( 24y = 0 \) by 24:
\[
y = \frac{0}{24} = 0
\]

Step3: Substitute \( y = 0 \) into one of the original equations (e.g., \( 2x + 9y = 24 \))

Substitute \( y = 0 \) into \( 2x + 9y = 24 \):
\[
2x + 9(0) = 24\\
2x + 0 = 24\\
2x = 24
\]

Step4: Solve for \( x \)

Divide both sides of \( 2x = 24 \) by 2:
\[
x = \frac{24}{2} = 12
\]

Answer:

\( x = 12 \)
\( y = 0 \)