Question

solve the system of equations.

• 5y + 8x = -18

5y + 2x = 58
x =

y =

Explanation:

Step1: Add the two equations

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

$$\begin{align*} (-5y + 8x) + (5y + 2x) &= -18 + 58\\ -5y + 8x + 5y + 2x &= 40\\ ( -5y + 5y)+(8x + 2x)&= 40\\ 10x&= 40 \end{align*}$$

\]

Step2: Solve for \( x \)

Divide both sides of the equation \( 10x = 40 \) by 10:
\[
x=\frac{40}{10} = 4
\]

Step3: Substitute \( x = 4 \) into one of the original equations (we'll use \( 5y + 2x = 58 \))

Substitute \( x = 4 \) into \( 5y+2x = 58 \):
\[

$$\begin{align*} 5y+2(4)&= 58\\ 5y + 8&= 58 \end{align*}$$

\]

Step4: Solve for \( y \)

Subtract 8 from both sides:
\[
5y=58 - 8=50
\]
Divide both sides by 5:
\[
y = \frac{50}{5}=10
\]

Answer:

\( x = 4 \)
\( y = 10 \)