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

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

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

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

(−2,3)
open paren negative 2 comma 3 close paren
Remaining Attempts : 3

Answer 1

To find the solution to the system of linear equations \( y = 3x + 1 \) and \( y = -2x - 4 \), we need to determine which point satisfies both equations.

Let's check each of the given points:

1. Point \((-1, -2)\):

   • For \( y = 3x + 1 \): \( y = 3(-1) + 1 = -3 + 1 = -2 \) → True.
   • For \( y = -2x - 4 \): \( y = -2(-1) - 4 = 2 - 4 = -2 \) → True.
   • This point satisfies both equations.

2. Point \((0, -4)\):

   • For \( y = 3x + 1 \): \( y = 3(0) + 1 = 0 + 1 = 1 \) → False.
   • This point does not satisfy the first equation.

3. Point \((0, 1)\):

   • For \( y = 3x + 1 \): \( y = 3(0) + 1 = 0 + 1 = 1 \) → True.
   • For \( y = -2x - 4 \): \( y = -2(0) - 4 = 0 - 4 = -4 \) → False.
   • This point does not satisfy the second equation.

4. Point \((-2, 3)\):

   • For \( y = 3x + 1 \): \( y = 3(-2) + 1 = -6 + 1 = -5 \) → False.
   • This point does not satisfy the first equation.

Based on the evaluations, the only point that satisfies both equations is \((-1, -2)\).

Thus, the correct answer is:

\((-1, -2)\)