Question

Solve the system by substitution.
9, x, plus, 3, y, equals, minus, 30
9x+3y=
−30
minus, 5, x, equals, y
−5x=
y

Answer 1

To solve the given system of equations by substitution, we first write the equations clearly:

1. \( 9x + 3y = -30 \)
2. \( y = -5x \)

Now, we can substitute the expression for \( y \) from the second equation into the first equation.

Substituting \( y = -5x \) into the first equation:

\[
9x + 3(-5x) = -30
\]

Now simplify the equation:

\[
9x - 15x = -30
\]

Combine like terms:

\[
-6x = -30
\]

Now, solve for \( x \):

\[
x = \frac{-30}{-6} = 5
\]

Now that we have the value of \( x \), we can substitute it back into the second equation to find \( y \):

\[
y = -5(5) = -25
\]

Now we have the solution:

\[
x = 5, \quad y = -25
\]

Thus, the solution to the system of equations is:

\[
(x, y) = (5, -25)
\]