Question

A graph shows two lines intersecting at (-1, -5) and two equations are given

Equation 1: y = 3x - 2
Equation 2: y = -x - 6

What is the solution to this system of linear equations?

(1 point)
Responses

Infinite solutions
Infinite solutions

(-1, -5)
(-1, -5)

(-6, 0)
(-6, 0)

No solution
No solution

(0, -2)
(0, -2)

Answer 1

To find the solution to the system of linear equations given by Equation 1: \( y = 3x - 2 \) and Equation 2: \( y = -x - 6 \), we can solve the system by checking if the lines intersect at a single point, which would be the solution to this system of equations.

The point of intersection is given as (-1, -5).

Now, we can check if this point satisfies both equations:

1. Substitute \( x = -1 \) into Equation 1:

\[
y = 3(-1) - 2 = -3 - 2 = -5
\]

This matches the point (-1, -5).

2. Substitute \( x = -1 \) into Equation 2:

\[
y = -(-1) - 6 = 1 - 6 = -5
\]

This also matches the point (-1, -5).

Since both equations are satisfied at the point (-1, -5), this means the two lines intersect at this point.

Thus, the solution to this system of linear equations is:

**(-1, -5)**