Question

Use the image to answer the 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

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

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

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

(−2,3)
open paren negative 2 comma 3 close paren
Remaining Attempts : 3
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Answer 1

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

1. **Point (0, 1)**:
- For \( y = 3x + 1 \):
\[
y = 3(0) + 1 = 1 \quad \text{(True)}
\]
- For \( y = -2x - 4 \):
\[
y = -2(0) - 4 = -4 \quad \text{(False)}
\]
- **This point does not satisfy both equations.**

2. **Point (0, -4)**:
- For \( y = 3x + 1 \):
\[
y = 3(0) + 1 = 1 \quad \text{(False)}
\]
- For \( y = -2x - 4 \):
\[
y = -2(0) - 4 = -4 \quad \text{(True)}
\]
- **This point does not satisfy both equations.**

3. **Point (-1, -2)**:
- For \( y = 3x + 1 \):
\[
y = 3(-1) + 1 = -3 + 1 = -2 \quad \text{(True)}
\]
- For \( y = -2x - 4 \):
\[
y = -2(-1) - 4 = 2 - 4 = -2 \quad \text{(True)}
\]
- **This point satisfies both equations.**

4. **Point (-2, 3)**:
- For \( y = 3x + 1 \):
\[
y = 3(-2) + 1 = -6 + 1 = -5 \quad \text{(False)}
\]
- For \( y = -2x - 4 \):
\[
y = -2(-2) - 4 = 4 - 4 = 0 \quad \text{(False)}
\]
- **This point does not satisfy both equations.**

After checking all the points, the only point that satisfies both equations \( y = 3x + 1 \) and \( y = -2x - 4 \) is:

**(-1, -2)**

Thus, the answer is **\((-1, -2)\)**.