Question

Here is a system of linear equations: y = x - 4 y = -3x - 8
What is the solution to the system of equations shown?
A.
(-3, 1)
B.
(1, -3)
C.
(-1, -5)
D.
(-5, -1)

Answer 1

To solve the system of linear equations given by:

1. \( y = x - 4 \)
2. \( y = -3x - 8 \)

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

\[
x - 4 = -3x - 8
\]

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

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

\[
x + 3x - 4 = -8
\]

\[
4x - 4 = -8
\]

2. Add \( 4 \) to both sides:

\[
4x = -8 + 4
\]

\[
4x = -4
\]

3. Divide by \( 4 \):

\[
x = -1
\]

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

\[
y = x - 4
\]

Substituting \( x = -1 \):

\[
y = -1 - 4 = -5
\]

So the solution to the system of equations is \( (x, y) = (-1, -5) \).

Therefore, the answer is:

**C. (-1, -5)**