Question

determine which ordered pair is a solution of the given system of equations.
y = 2x - 5
y = 4x - 7
○ (-1, 3)
○ (1, -3)
○ (2, 2)
○ (0, -5)

Explanation:

Step1: Set the two equations equal

Since both equal \( y \), set \( 2x - 5 = 4x - 7 \).

Step2: Solve for \( x \)

Subtract \( 2x \) from both sides: \( -5 = 2x - 7 \).
Add 7 to both sides: \( 2 = 2x \).
Divide by 2: \( x = 1 \).

Step3: Find \( y \)

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

Step4: Verify with the second equation

Substitute \( x = 1 \), \( y = -3 \) into \( y = 4x - 7 \): \( -3 = 4(1) - 7 = -3 \). It works.

Answer:

\( (1, -3) \)