Question

solve the system of equations graphed on the coordinate axes below.
$y = \frac{4}{3}x - 3$
$y = -\frac{3}{4}x - 3$

Explanation:

Step1: Set the equations equal

Since both equations equal \( y \), set \( \frac{4}{3}x - 3 = -\frac{3}{4}x - 3 \).

Step2: Solve for \( x \)

Add \( 3 \) to both sides: \( \frac{4}{3}x = -\frac{3}{4}x \).
Multiply both sides by \( 12 \) (LCM of 3,4) to eliminate denominators: \( 16x = -9x \).
Add \( 9x \) to both sides: \( 25x = 0 \), so \( x = 0 \).

Step3: Find \( y \)

Substitute \( x = 0 \) into \( y = \frac{4}{3}x - 3 \): \( y = 0 - 3 = -3 \).

Answer:

The solution is \( (0, -3) \)