Question

the equations $y = -2x - 4$ and $y = 3x + 1$ are shown in the graph. which is the solution to the system of equations? (1 point) $\bigcirc$ $(-2, -1)$ $\bigcirc$ $(-2, 1)$ $\bigcirc$ $(-1, -2)$ $\bigcirc$ $(1, -2)$

Explanation:

Step1: Recall solution of system

The solution to a system of linear equations is the point where their graphs intersect.

Step2: Identify intersection point

Looking at the graph, the two lines \( y = -2x - 4 \) and \( y = 3x + 1 \) intersect at the point with \( x = -1 \) and \( y = -2 \), which is \( (-1, -2) \). We can also verify by substituting into both equations:

• For \( y = -2x - 4 \): Substitute \( x = -1 \), \( y = -2(-1)-4 = 2 - 4 = -2 \), which matches.
• For \( y = 3x + 1 \): Substitute \( x = -1 \), \( y = 3(-1)+1 = -3 + 1 = -2 \), which also matches.

Answer:

C. \((-1, -2)\) (assuming the options are labeled as A. \((-2, -1)\), B. \((-2, 1)\), C. \((-1, -2)\), D. \((1, -2)\))