Question

solve the system of equations by substitution.
-4x + 4y = -40
y = 3x - 4

Answer 1

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

1. \(-4x + 4y = -40\)
2. \(y = 3x - 4\)

We can substitute the expression for \(y\) from the second equation into the first equation.

Substituting \(y\) in the first equation:

\[
-4x + 4(3x - 4) = -40
\]

Now, distribute the 4:

\[
-4x + 12x - 16 = -40
\]

Combine like terms:

\[
(12x - 4x) - 16 = -40
\]

\[
8x - 16 = -40
\]

Now, add 16 to both sides:

\[
8x = -40 + 16
\]

\[
8x = -24
\]

Next, divide both sides by 8:

\[
x = -3
\]

Now that we have \(x\), we substitute it back into the second equation to find \(y\):

\[
y = 3(-3) - 4
\]

\[
y = -9 - 4
\]

\[
y = -13
\]

The solution to the system of equations is:

\[
(x, y) = (-3, -13)
\]