To solve the system of equations using the substitution method, we start with the two equations given:
- \( 9x - 3y = 12 \) (Equation 1)
- \( y + 6 = 2x \) (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:
\[ \boxed{(-2, -10)} \]
1 answer