Question

Use substitution to solve the system of equations.

5x + y = –24
x + 3y = –2
x = –5, y = –1
x = 5, y = 1
x = –5, y = 1
x = 5, y = –1

Answer 1

To solve the system of equations using substitution, we start with the two equations:

1. \( 5x + y = -24 \) (Equation 1)
2. \( x + 3y = -2 \) (Equation 2)

First, we can solve Equation 1 for \( y \):

\[
y = -24 - 5x
\]

Now, we substitute this expression for \( y \) into Equation 2:

\[
x + 3(-24 - 5x) = -2
\]

Simplifying this equation:

\[
x - 72 - 15x = -2
\]
\[
-14x - 72 = -2
\]

Now, isolate the \( x \) term:

\[
-14x = -2 + 72
\]
\[
-14x = 70
\]
\[
x = \frac{70}{-14}
\]
\[
x = -5
\]

Now that we have \( x \), we can substitute this value back into the equation we derived for \( y \):

\[
y = -24 - 5(-5)
\]
\[
y = -24 + 25
\]
\[
y = 1
\]

Thus, the solution to the system of equations is:

\[
x = -5, \quad y = 1
\]

So the correct answer is:

\[
\textbf{x = -5, y = 1}
\]