Use the image to answer the question.

Question

A coordinate graph goes from negative 10 to 10 in 1-unit increments on both the x- and y-axes. Two linear equations are graphed, along with four points.

The system of linear equations {y=3x+1y=−2x−4
is shown. Which of the points on the graph represents the solution to the linear system?

(1 point)
Responses

(0,−4)
open paren 0 comma negative 4 close paren

(−1,−2)
open paren negative 1 comma negative 2 close paren

(0,1)
open paren 0 comma 1 close paren

(−2,3)

Answer 1

To determine the solution to the system of linear equations represented by the points given, we need to check which of the points satisfies both equations in the system:

1. The equations are:

   • \( y = 3x + 1 \)
   • \( y = -2x - 4 \)

2. We will evaluate each point to see if it satisfies both equations.

Checking the points:

1. For (0, -4):

   • Substitute \( x = 0 \) in both equations:
     • \( y = 3(0) + 1 = 1 \) (not -4)
     • \( y = -2(0) - 4 = -4 \) (matches second equation)
   • Does not satisfy both.

2. For (-1, -2):

   • Substitute \( x = -1 \):
     • \( y = 3(-1) + 1 = -2 \) (matches first equation)
     • \( y = -2(-1) - 4 = 2 - 4 = -2 \) (matches second equation)
   • Satisfies both.

3. For (0, 1):

   • Substitute \( x = 0 \):
     • \( y = 3(0) + 1 = 1 \) (matches first equation)
     • \( y = -2(0) - 4 = -4 \) (not 1)
   • Does not satisfy both.

4. For (-2, 3):

   • Substitute \( x = -2 \):
     • \( y = 3(-2) + 1 = -6 + 1 = -5 \) (not 3)
     • \( y = -2(-2) - 4 = 4 - 4 = 0 \) (not 3)
   • Does not satisfy both.

Conclusion:

The point that satisfies both equations is (−1,−2).