Question

1. which ordered pair is a solution for the system of linear equations shown? \\(\

$$\begin{cases}4x + 3y = -9 \\\\ y = 2x - 13\\end{cases}$$

\\) \\(\bigcirc\\ (3, 7)\\) \\(\bigcirc\\ (-3, 7)\\) \\(\bigcirc\\ (3, -7)\\) \\(\bigcirc\\ (-3, -7)\\)

Explanation:

Step1: Substitute \( y = 2x - 13 \) into \( 4x + 3y = -9 \)

Substitute \( y \) in the first equation: \( 4x + 3(2x - 13) = -9 \)

Step2: Simplify the equation

Expand and combine like terms: \( 4x + 6x - 39 = -9 \) → \( 10x - 39 = -9 \)

Step3: Solve for \( x \)

Add 39 to both sides: \( 10x = 30 \) → \( x = 3 \)

Step4: Find \( y \) using \( x = 3 \)

Substitute \( x = 3 \) into \( y = 2x - 13 \): \( y = 2(3) - 13 = 6 - 13 = -7 \)

Answer:

(3, -7)