Question

GG.8 Solve a system of equations using substitution
J8X
Solve using substitution.

2x − 6y = –8
x − 4y = –8

Answer 1

To solve the system of equations using substitution, we have the following equations:

1. \( 2x - 6y = -8 \) (Equation 1)
2. \( x - 4y = -8 \) (Equation 2)

We can start with Equation 2 and solve for \( x \):

\[
x = 4y - 8
\]

Now that we have \( x \) in terms of \( y \), we can substitute this expression into Equation 1:

\[
2(4y - 8) - 6y = -8
\]

Next, simplify and solve for \( y \):

1. Distribute \( 2 \) in the first term:

\[
8y - 16 - 6y = -8
\]

2. Combine like terms:

\[
2y - 16 = -8
\]

3. Add \( 16 \) to both sides:

\[
2y = 8
\]

4. Divide by \( 2 \):

\[
y = 4
\]

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

\[
x = 4(4) - 8
\]

Calculate \( x \):

\[
x = 16 - 8 = 8
\]

Thus, the solution to the system of equations is:

\[
(x, y) = (8, 4)
\]

To verify, plug the values back into the original equations:

1. For Equation 1:
\[
2(8) - 6(4) = 16 - 24 = -8 \quad \text{(True)}
\]

2. For Equation 2:
\[
8 - 4(4) = 8 - 16 = -8 \quad \text{(True)}
\]

Both equations hold true, confirming that the solution is correct.

The solution is:

\[
\boxed{(8, 4)}
\]