Question

solve the system of equations graphed on the coordinate axes below.
y = -x + 3
y = 3x + 7

Explanation:

Step1: Set the two equations equal

Since both equations are solved for \( y \), we can set them equal to each other: \(-x + 3 = 3x + 7\)

Step2: Solve for \( x \)

Add \( x \) to both sides: \( 3 = 4x + 7 \)
Subtract 7 from both sides: \( -4 = 4x \)
Divide by 4: \( x = -1 \)

Step3: Substitute \( x \) back to find \( y \)

Substitute \( x = -1 \) into \( y = -x + 3 \): \( y = -(-1) + 3 = 1 + 3 = 4 \)

Answer:

The solution to the system is \( x = -1 \), \( y = 4 \) (or the ordered pair \((-1, 4)\))