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

Answer 1

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

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

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

Substituting \( y \):

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

Now, simplify the equation:

\[
x + 77x - 583 = 119
\]
\[
78x - 583 = 119
\]

Next, isolate \( x \):

\[
78x = 119 + 583
\]
\[
78x = 702
\]
\[
x = \frac{702}{78} = 9
\]

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

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

Thus, the solution to the system of equations is:

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