Question

Solve the system by substitution.
6x - 2y = -4
y = -6x + 20

Answer 1

To solve the system of equations using substitution, we follow these steps:

1. We already have one equation solved for \( y \):
\[
y = -6x + 20
\]

2. We can substitute this expression for \( y \) into the first equation \( 6x - 2y = -4 \):
\[
6x - 2(-6x + 20) = -4
\]

3. Now, simplify the equation:
\[
6x + 12x - 40 = -4
\]
\[
18x - 40 = -4
\]

4. Next, add 40 to both sides:
\[
18x = -4 + 40
\]
\[
18x = 36
\]

5. Now, divide by 18 to find \( x \):
\[
x = \frac{36}{18} = 2
\]

6. Now that we have the value of \( x \), we can substitute it back into the second equation to find \( y \):
\[
y = -6(2) + 20
\]
\[
y = -12 + 20
\]
\[
y = 8
\]

7. Thus, the solution to the system of equations is:
\[
(x, y) = (2, 8)
\]

So the final answer is:
\[
\boxed{(2, 8)}
\]