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)

$\bigcirc\\ (-2, 1)$

$\bigcirc\\ (-1, 2)$

$\bigcirc\\ (2, -1)$

$\bigcirc\\ (1, -2)$

Explanation:

Step1: Recall solution of system

The solution of a system of linear equations (when graphed) is the point of intersection of the two lines. So we need to find the point where \( y = 2x + 4 \) and \( y=-3x - 1 \) intersect.

Step2: Analyze the graph

Looking at the graph, the two lines intersect at a point. Let's check the coordinates. From the grid, the x - coordinate is - 1 and the y - coordinate is 2. We can also verify by substituting into the equations:
For \( y = 2x+4 \), when \( x=-1 \), \( y=2\times(-1)+4=-2 + 4=2 \)
For \( y=-3x - 1 \), when \( x = - 1 \), \( y=-3\times(-1)-1=3 - 1=2 \)
So the point of intersection (solution) is \( (-1,2) \)

Answer:

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