Question

solve the system of equations.
$y = x + 16$
$y = 5x - 12$
$x = \boxed{}$
$y = \boxed{}$

Explanation:

Step1: Set the two equations equal

Since both equations equal \( y \), we can set them equal to each other: \( x + 16 = 5x - 12 \)

Step2: Solve for \( x \)

Subtract \( x \) from both sides: \( 16 = 4x - 12 \)
Add 12 to both sides: \( 28 = 4x \)
Divide by 4: \( x = 7 \)

Step3: Solve for \( y \)

Substitute \( x = 7 \) into \( y = x + 16 \): \( y = 7 + 16 = 23 \)

Answer:

\( x = 7 \)
\( y = 23 \)