Question

1. find the solution to the system of equations.

$y = 3x - 4$
$y = -2x + 6$
a $(2, -2)$ c $(0.4, -2.8)$
b $(-2, -10)$ d $(2, 2)$

Explanation:

Step1: Set equations equal

Since \( y = 3x - 4 \) and \( y = -2x + 6 \), set \( 3x - 4 = -2x + 6 \).

Step2: Solve for x

Add \( 2x \) to both sides: \( 3x + 2x - 4 = 6 \) → \( 5x - 4 = 6 \).
Add 4 to both sides: \( 5x = 6 + 4 \) → \( 5x = 10 \).
Divide by 5: \( x = \frac{10}{5} = 2 \).

Step3: Find y

Substitute \( x = 2 \) into \( y = 3x - 4 \): \( y = 3(2) - 4 = 6 - 4 = 2 \).

Answer:

D. (2, 2)