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
Y=-13X-27
Y=X+1

Answer 1

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

1. \( Y = -13X - 27 \) (Equation 1)
2. \( Y = X + 1 \) (Equation 2)

Since both equations define \( Y \), we can set them equal to each other:

\[
-13X - 27 = X + 1
\]

Now, we'll solve for \( X \):

1. Add \( 13X \) to both sides:
\[
-27 = 14X + 1
\]

2. Subtract 1 from both sides:
\[
-28 = 14X
\]

3. Divide by 14:
\[
X = -2
\]

Now that we have found \( X \), let's use Equation 2 to find \( Y \):

\[
Y = X + 1 = -2 + 1 = -1
\]

Thus, the solution to the system of equations is:

\[
\boxed{(-2, -1)}
\]