Question

system of equation
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
solution

Answer 1

To solve the system of equations using the substitution method, we have the following two equations:

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

We can substitute the expression for \( x \) from the first equation into the second equation:

Substituting \( x = -4y - 28 \) into the second equation:

\[
-13(-4y - 28) + y = 99
\]
Now, simplify the equation:

\[
52y + 364 + y = 99
\]
Combine like terms:

\[
53y + 364 = 99
\]
Next, isolate \( y \):

\[
53y = 99 - 364
\]
\[
53y = -265
\]
Now, divide both sides by 53:

\[
y = -\frac{265}{53}
\]
Calculating \( -\frac{265}{53} \):

\[
y = -5
\]

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

\[
x = -4(-5) - 28
\]
\[
x = 20 - 28
\]
\[
x = -8
\]

Thus, the solution to the system of equations is:

\[
\text{Ordered Pair: } (-8, -5)
\]