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

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

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

(−2,3)

Answer 1

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

1. Check (0, -4):

   • For \( y = 3x + 1 \): \[ -4 = 3(0) + 1 \Rightarrow -4 \neq 1 \]
   • This point does not satisfy the first equation.

2. Check (0, 1):

   • For \( y = 3x + 1 \): \[ 1 = 3(0) + 1 \Rightarrow 1 = 1 \]
   • This point satisfies the first equation.
   • Now check the second equation: \[ 1 = -2(0) - 4 \Rightarrow 1 \neq -4 \]
   • This point does not satisfy the second equation.

3. Check (-1, -2):

   • For \( y = 3x + 1 \): \[ -2 = 3(-1) + 1 \Rightarrow -2 = -3 + 1 \Rightarrow -2 = -2 \]
   • This point satisfies the first equation.
   • Now check the second equation: \[ -2 = -2(-1) - 4 \Rightarrow -2 = 2 - 4 \Rightarrow -2 = -2 \]
   • This point satisfies both equations.

4. Check (-2, 3):

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

From our checks, the only point that satisfies both equations is (-1, -2).

So the answer is: (−1,−2).