Question

Solve the system by substitution.
y, equals, minus, 9, x
y=
−9x
y, equals, 2, x, plus, 33
y=
2x+33

Answer 1

To solve the system of equations by substitution, we have the following two equations:

1. \( y = -9x \)
2. \( y = 2x + 33 \)

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

\[
-9x = 2x + 33
\]

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

1. Add \( 9x \) to both sides:

\[
-9x + 9x = 2x + 33 + 9x
\]
\[
0 = 11x + 33
\]

2. Subtract 33 from both sides:

\[
-33 = 11x
\]

3. Divide by 11:

\[
x = -3
\]

Now that we have \( x \), we can find \( y \) using the first equation:

\[
y = -9x
\]
\[
y = -9(-3) = 27
\]

So the solution to the system of equations is:

\[
(x, y) = (-3, 27)
\]

**Final result:** The solution is \( x = -3 \) and \( y = 27 \).