Question

which point is a solution of the system of equations shown?
y = -3x + 5
y = 4x - 9
○ (2, -1)
○ (12, 39)
○ (7, -16)
○ (-1, 8)

Explanation:

Step1: Set the equations equal

Since both equal \( y \), set \( -3x + 5 = 4x - 9 \).

Step2: Solve for \( x \)

Add \( 3x \) to both sides: \( 5 = 7x - 9 \).
Add 9 to both sides: \( 14 = 7x \).
Divide by 7: \( x = 2 \).

Step3: Find \( y \)

Substitute \( x = 2 \) into \( y = -3x + 5 \):
\( y = -3(2) + 5 = -6 + 5 = -1 \).

Step4: Verify the point

The point is \( (2, -1) \). Check in \( y = 4x - 9 \): \( 4(2) - 9 = 8 - 9 = -1 \), which matches.

Answer:

A. (2, -1)