Question

Solve using substitution.
x+2y=7
2x-y=-16

Answer 1

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

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

First, 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:

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

Now distribute the \( 2 \):

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

Combine like terms:

\[
14 - 5y = -16
\]

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

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

Now, divide both sides by -5:

\[
y = \frac{-30}{-5} = 6
\]

Now that we have the value of \( y \), we can 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

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

So the final answer is:

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