Question

Question

What is the solution to this system of linear equations?
y = 3x - 2
y = -x - 6
Systems of Linear Equations: Definitions | Purplemath

(1 point)
Responses

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

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

No solution
No solution

Infinite solutions
Infinite solutions

(0, -2)
(0, -2)
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Answer 1

To solve the system of equations given:

1. \( y = 3x - 2 \)
2. \( y = -x - 6 \)

We can set the two expressions for \( y \) equal to each other since they are both equal to \( y \):

\[ 3x - 2 = -x - 6 \]

Now, let's solve for \( x \):

1. Add \( x \) to both sides: \[ 3x + x - 2 = -6 \] \[ 4x - 2 = -6 \]

2. Add 2 to both sides: \[ 4x = -6 + 2 \] \[ 4x = -4 \]

3. Divide both sides by 4: \[ x = -1 \]

Now that we have \( x = -1 \), we can substitute this value back into either of the original equations to find \( y \). We'll use the first equation:

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

So the solution to the system of equations is:

(-1, -5)

This matches the first option provided in your responses.