Question

Solve using substitution.

5x + y = –12
4x − y = 3

(
,
)

Answer 1

To solve the system of equations using substitution, we first need to express one variable in terms of the other using one of the equations.

We have the two equations:

1. \( 5x + y = -12 \) (Equation 1)
2. \( 4x - y = 3 \) (Equation 2)

Let's solve Equation 1 for \( y \):

\[ y = -12 - 5x \]

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

\[ 4x - (-12 - 5x) = 3 \]

This simplifies to:

\[ 4x + 12 + 5x = 3 \]

Combine like terms:

\[ 9x + 12 = 3 \]

Now, isolate \( x \):

\[ 9x = 3 - 12 \]
\[ 9x = -9 \]
\[ x = -1 \]

Now that we have \( x \), we can substitute it back into the expression we found for \( y \):

\[ y = -12 - 5(-1) \]
\[ y = -12 + 5 \]
\[ y = -7 \]

Thus, the solution to the system of equations is:

\[
(x, y) = (-1, -7)
\]

So your final answer is:

\[
(-1, -7)
\]