Question

Solve using substitution.

2x + y = –14
10x − 4y = 2

Answer 1

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

1) \( 2x + y = -14 \)
2) \( 10x - 4y = 2 \)

First, we can solve the first equation for \( y \):

\[
y = -14 - 2x
\]

Next, we will substitute this expression for \( y \) into the second equation.

Substituting \( y \) in equation 2:

\[
10x - 4(-14 - 2x) = 2
\]

Now, we will simplify this equation:

\[
10x + 56 + 8x = 2
\]

Combine like terms:

\[
18x + 56 = 2
\]

Next, isolate \( x \) by subtracting 56 from both sides:

\[
18x = 2 - 56
\]
\[
18x = -54
\]

Now, divide by 18:

\[
x = \frac{-54}{18} = -3
\]

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

\[
y = -14 - 2(-3)
\]
\[
y = -14 + 6
\]
\[
y = -8
\]

We have found \( x \) and \( y \):

\[
x = -3, \quad y = -8
\]

Thus, the solution to the system of equations is:

\[
(x, y) = (-3, -8)
\]

To verify, let's plug \( x \) and \( y \) back into both original equations:

1) \( 2(-3) + (-8) = -6 - 8 = -14 \) (True)
2) \( 10(-3) - 4(-8) = -30 + 32 = 2 \) (True)

Both equations are satisfied, confirming our solution is correct. The final solution is:

\[
\boxed{(-3, -8)}
\]