Use the substitution method to solve the system 9x−3y=12

Question

, y+6=2x
.(1 point)
(
)

Answer 1

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

1. \( 9x - 3y = 12 \)

2. \( y + 6 = 2x \)

Let's start with Equation 2 to express \( y \) in terms of \( x \):

\[ y + 6 = 2x \]

Now, isolate \( y \):

\[ y = 2x - 6 \]

Next, we will substitute this expression for \( y \) into Equation 1:

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

Now, distribute the \(-3\):

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

Combine like terms:

\[ 3x + 18 = 12 \]

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

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

Now divide by 3:

\[ x = -2 \]

Next, substitute \( x = -2 \) back into the expression for \( y \):

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

Thus, the solution to the system of equations is:

\[ (x, y) = (-2, -10) \]

The final answer is \((-2, -10)\).