Question

solve the system of equations graphed on the coordinate axes below.
y = x - 2
y = -\frac{1}{5}x - 2

Explanation:

Step1: Set the equations equal

Since both equal \( y \), set \( x - 2 = -\frac{1}{5}x - 2 \).

Step2: Solve for \( x \)

Add \( \frac{1}{5}x \) to both sides: \( x+\frac{1}{5}x - 2 = - 2 \).
Combine like terms: \( \frac{6}{5}x - 2 = - 2 \).
Add 2 to both sides: \( \frac{6}{5}x = 0 \).
Multiply both sides by \( \frac{5}{6} \): \( x = 0 \).

Step3: Find \( y \)

Substitute \( x = 0 \) into \( y = x - 2 \): \( y = 0 - 2 = -2 \).

Answer:

The solution is \( (0, -2) \)