Question

solve this system of equations.
y = 4x + 8
y = 2x + 16
use the sketch tool or paper if it helps with your thinking.

Explanation:

Step1: Set the two equations equal

Since both equations equal \( y \), we can set \( 4x + 8 = 2x + 16 \).

Step2: Solve for \( x \)

Subtract \( 2x \) from both sides: \( 4x - 2x + 8 = 2x - 2x + 16 \), which simplifies to \( 2x + 8 = 16 \). Then subtract 8 from both sides: \( 2x + 8 - 8 = 16 - 8 \), so \( 2x = 8 \). Divide both sides by 2: \( \frac{2x}{2} = \frac{8}{2} \), giving \( x = 4 \).

Step3: Find \( y \)

Substitute \( x = 4 \) into \( y = 4x + 8 \): \( y = 4(4) + 8 = 16 + 8 = 24 \).

Answer:

The solution to the system is \( x = 4 \), \( y = 24 \) (or the ordered pair \( (4, 24) \))