Question

Solve the system of equations by substitution. −4x+4y=−40. y=3x−4.
This question requires you to show your work.
(−3,−13) (3, 7) (6, 4) (1,−1)

Answer 1

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

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

### Step 1: Substitute Equation 2 into Equation 1

We substitute \( y \) from Equation 2 into Equation 1. So we replace \( y \) in Equation 1:

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

### Step 2: Simplify the Equation

Now we simplify the equation:

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

Combine like terms:

\[
8x - 16 = -40
\]

### Step 3: Add 16 to Both Sides

Now add 16 to both sides:

\[
8x = -40 + 16
\]

\[
8x = -24
\]

### Step 4: Divide by 8

Now, divide both sides by 8:

\[
x = -3
\]

### Step 5: Substitute \( x \) back into Equation 2 to find \( y \)

Now that we have \( x = -3 \), we substitute it back into Equation 2 to find \( y \):

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

\[
y = -9 - 4
\]

\[
y = -13
\]

### Step 6: Conclusion

The solution to the system of equations is:

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

### Verification

To verify, we can check if the values satisfy both original equations.

1. Substituting into Equation 1:

\[
-4(-3) + 4(-13) = 12 - 52 = -40 \quad \text{(True)}
\]

2. Substituting into Equation 2:

\[
y = 3(-3) - 4 = -9 - 4 = -13 \quad \text{(True)}
\]

Thus, the solution \((-3, -13)\) satisfies both equations.

### Final Answer

The solution to the system of equations is:

\[
\boxed{(-3, -13)}
\]