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:

$$
LATEXBLOCK0
$$

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 \( 5y+2x = 58 \):

$$
LATEXBLOCK1
$$

Step4: Solve for \( y \)

Subtract 8 from both sides:

$$ 5y=58 - 8=50 $$

Divide both sides by 5:

$$ y = \frac{50}{5}=10 $$

Answer:

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