Question

Question Use the substitution method to solve the system 9x−3y=12 , y+6=2x .(1 point)

Answer 1

To solve the system of equations using the substitution method, we start with the two equations given:

1. \( 9x - 3y = 12 \) (Equation 1)
2. \( y + 6 = 2x \) (Equation 2)

First, we'll solve Equation 2 for \( y \):

\[
y = 2x - 6
\]

Next, we'll substitute \( y \) in Equation 1 with the expression we found from Equation 2:

\[
9x - 3(2x - 6) = 12
\]

Now, distribute \(-3\) in the equation:

\[
9x - 6x + 18 = 12
\]

Combine like terms:

\[
3x + 18 = 12
\]

Now, isolate \( x \) by subtracting 18 from both sides:

\[
3x = 12 - 18
\]
\[
3x = -6
\]

Now divide both sides by 3:

\[
x = -2
\]

Now that we have \( x \), we will substitute \( x = -2 \) back into the expression we found for \( y \):

\[
y = 2(-2) - 6
\]
\[
y = -4 - 6
\]
\[
y = -10
\]

Now we have our solution:

\[
x = -2, \quad y = -10
\]

Thus, the solution to the system of equations is:

\[
\boxed{(-2, -10)}
\]