Question

Identify the solution to the system of linear equations.

y = -3x + 2

y = x - 6

Responses

(2, -4)
(2, -4)

(4, -2)
(4, -2)

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

(0, 2)

Answer 1

To find the solution to the system of linear equations given by:

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

We can set the two equations equal to each other since both expressions represent \( y \):

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

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

1. Add \( 3x \) to both sides:

\[
2 = 4x - 6
\]

2. Add \( 6 \) to both sides:

\[
8 = 4x
\]

3. Divide both sides by \( 4 \):

\[
x = 2
\]

Now that we have \( x \), we can substitute it back into either of the original equations to find \( y \). We'll use the second equation:

\[
y = 2 - 6
\]
\[
y = -4
\]

Thus, the solution to the system of equations is \( (2, -4) \).

Checking with the first equation:

\[
y = -3(2) + 2 = -6 + 2 = -4
\]

Both equations give \( y = -4 \) when \( x = 2 \), confirming the solution.

The answer is \( \boxed{(2, -4)} \).