Question

Solve the following system of equations with the substitution method. Write your answers as an Ordered Pair. If infinitely many solutions exist, enter
(oo). If no solution exists, enter DNE
x= -4y - 28
-13x + y =99

Answer 1

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

1. \( x = -4y - 28 \) (Equation 1)
2. \( -13x + y = 99 \) (Equation 2)

Next, we substitute the expression for \( x \) from Equation 1 into Equation 2.

Substitute \( x \) in Equation 2:
\[
-13(-4y - 28) + y = 99
\]

Now simplify the equation:
\[
52y + 364 + y = 99
\]
Combine like terms:
\[
53y + 364 = 99
\]

Next, isolate \( y \) by subtracting 364 from both sides:
\[
53y = 99 - 364
\]
\[
53y = -265
\]

Now solve for \( y \) by dividing both sides by 53:
\[
y = \frac{-265}{53}
\]
\[
y = -5
\]

Now that we have \( y \), substitute \( y = -5 \) back into Equation 1 to find \( x \):
\[
x = -4(-5) - 28
\]
\[
x = 20 - 28
\]
\[
x = -8
\]

Thus, the solution to the system of equations is:
\[
(x, y) = (-8, -5)
\]

The final answer as an ordered pair is:
\[
\boxed{(-8, -5)}
\]