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
y = -15x-6
y=5x+14

Answer 1

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

1. \( y = -15x - 6 \)
2. \( y = 5x + 14 \)

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

\[
-15x - 6 = 5x + 14
\]

Now, let's solve for \( x \):

1. Add \( 15x \) to both sides:
\[
-6 = 20x + 14
\]

2. Subtract \( 14 \) from both sides:
\[
-6 - 14 = 20x
\]
\[
-20 = 20x
\]

3. Divide by \( 20 \):
\[
x = -1
\]

Now that we have \( x \), we can substitute it back into one of the original equations to find \( y \). We'll use the second equation:

\[
y = 5(-1) + 14
\]
\[
y = -5 + 14
\]
\[
y = 9
\]

Thus, the solution to the system of equations is:

\[
\boxed{(-1, 9)}
\]