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+17y=50
y=-14x-11

Answer 1

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

1. \( x + 17y = 50 \) (Equation 1)
2. \( y = -14x - 11 \) (Equation 2)

We can substitute the expression for \( y \) from Equation 2 into Equation 1.

Substituting \( y = -14x - 11 \) into Equation 1:

\[
x + 17(-14x - 11) = 50
\]

Now, distribute \( 17 \):

\[
x - 238x - 187 = 50
\]

Combine like terms:

\[
-237x - 187 = 50
\]

Add 187 to both sides:

\[
-237x = 237
\]

Now, divide both sides by -237:

\[
x = -1
\]

Now that we have \( x = -1 \), we can substitute this value back into Equation 2 to find \( y \):

\[
y = -14(-1) - 11
\]

Calculate \( y \):

\[
y = 14 - 11 = 3
\]

The solution to the system of equations is \( (x, y) = (-1, 3) \).

Thus, the answer as an Ordered Pair is:

\[
\boxed{(-1, 3)}
\]