Question

Solve using substitution.

x + 2y = 7
2x − y = –16

Answer 1

To solve the system of equations using substitution, we'll start with the given equations:

1. \( x + 2y = 7 \) (Equation 1)
2. \( 2x - y = -16 \) (Equation 2)

First, we will solve Equation 1 for \( x \):

\[
x = 7 - 2y
\]

Now that we have \( x \) in terms of \( y \), we can substitute this expression for \( x \) into Equation 2.

Substituting \( x = 7 - 2y \) into Equation 2:

\[
2(7 - 2y) - y = -16
\]

Now, simplify this equation:

\[
14 - 4y - y = -16
\]

Combine like terms:

\[
14 - 5y = -16
\]

Next, isolate \( y \) by subtracting 14 from both sides:

\[
-5y = -16 - 14
\]
\[
-5y = -30
\]

Now, divide by -5:

\[
y = 6
\]

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

\[
x = 7 - 2(6)
\]
\[
x = 7 - 12
\]
\[
x = -5
\]

Thus, the solution to the system of equations is:

\[
x = -5, \quad y = 6
\]

We can write the solution as an ordered pair:

\[
(-5, 6)
\]

To verify, we can substitute \( x \) and \( y \) back into the original equations:

1. For \( x + 2y = 7 \):
\[
-5 + 2(6) = -5 + 12 = 7 \quad \text{(True)}
\]

2. For \( 2x - y = -16 \):
\[
2(-5) - 6 = -10 - 6 = -16 \quad \text{(True)}
\]

Both equations are satisfied, confirming that the solution is indeed:

\[
\boxed{(-5, 6)}
\]