Question

solve the system of equations graphed on the coordinate axes below.
y = x + 2
y = -5x + 8

Explanation:

Step1: Set the two equations equal

Since both equations are solved for \( y \), we can set them equal to each other: \( x + 2 = -5x + 8 \)

Step2: Solve for \( x \)

Add \( 5x \) to both sides: \( x + 5x + 2 = -5x + 5x + 8 \) which simplifies to \( 6x + 2 = 8 \)
Subtract 2 from both sides: \( 6x + 2 - 2 = 8 - 2 \) which gives \( 6x = 6 \)
Divide both sides by 6: \( \frac{6x}{6} = \frac{6}{6} \) so \( x = 1 \)

Step3: Find \( y \) by substituting \( x = 1 \) into \( y = x + 2 \)

Substitute \( x = 1 \) into \( y = x + 2 \): \( y = 1 + 2 = 3 \)

Answer:

The solution to the system of equations is \( x = 1 \), \( y = 3 \) or the ordered pair \( (1, 3) \)