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

Answer 1

To solve the system of equations using the substitution method, we can use the first equation to substitute for \( y \) in the second equation.

The given equations are:

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

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

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

Next, we'll solve for \( x \). First, we can add \( 15x \) to both sides:

\[
-6 = 20x + 14
\]

Now, subtract 14 from both sides:

\[
-6 - 14 = 20x
\]

\[
-20 = 20x
\]

Now, divide both sides 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 first equation:

\[
y = -15(-1) - 6
\]

\[
y = 15 - 6
\]

\[
y = 9
\]

Thus, the solution to the system of equations is \((x, y) = (-1, 9)\).

The answer in ordered pair form is:

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