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-11y = 119
y=-7x+53

Answer 1

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

1. \( x - 11y = 119 \)
2. \( y = -7x + 53 \)

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

Substituting \( y = -7x + 53 \) into the first equation gives us:

\[
x - 11(-7x + 53) = 119
\]

Now, distribute the \(-11\):

\[
x + 77x - 583 = 119
\]

Combine like terms:

\[
78x - 583 = 119
\]

Next, add \( 583 \) to both sides:

\[
78x = 119 + 583
\]

Calculate \( 119 + 583 \):

\[
78x = 702
\]

Now, divide both sides by \( 78 \):

\[
x = \frac{702}{78} = 9
\]

Now that we have \( x \), we can find \( y \) by substituting \( x \) back into the equation for \( y \):

\[
y = -7(9) + 53
\]
\[
y = -63 + 53
\]
\[
y = -10
\]

The solution to the system of equations is \( (x, y) = (9, -10) \).

Thus, the answer in ordered pair form is:

\[
\boxed{(9, -10)}
\]