Question

solve the system.
y = x - 3
y = -2x + 3

Explanation:

Step1: Set the two equations equal

Since both equations equal \( y \), we can set them equal to each other: \( x - 3 = -2x + 3 \)

Step2: Solve for \( x \)

Add \( 2x \) to both sides: \( 3x - 3 = 3 \)
Add \( 3 \) to both sides: \( 3x = 6 \)
Divide by \( 3 \): \( x = 2 \)

Step3: Substitute \( x \) into one equation

Use \( y = x - 3 \), substitute \( x = 2 \): \( y = 2 - 3 = -1 \)

Answer:

The solution to the system is \( x = 2 \), \( y = -1 \)