To solve the system of equations given by:
- \( -9x + y = 12 \) (Equation 1)
- \( 2x + 4y = -28 \) (Equation 2)
we can use substitution or elimination. Let's use substitution for this example.
Step 1: Solve Equation 1 for \( y \)
From Equation 1: \[ y = 9x + 12 \]
Step 2: Substitute \( y \) from Equation 1 into Equation 2
Substituting \( y \) into Equation 2: \[ 2x + 4(9x + 12) = -28 \]
Step 3: Simplify the equation
Expanding the equation: \[ 2x + 36x + 48 = -28 \] \[ 38x + 48 = -28 \]
Step 4: Solve for \( x \)
Subtract 48 from both sides: \[ 38x = -28 - 48 \] \[ 38x = -76 \] \[ x = -\frac{76}{38} = -2 \]
Step 5: Substitute \( x \) back into the equation for \( y \)
Using \( x = -2 \) in \( y = 9x + 12 \): \[ y = 9(-2) + 12 \] \[ y = -18 + 12 \] \[ y = -6 \]
Final Answer:
The solution to the system of equations is: \[ (x, y) = (-2, -6) \]
So, the answer is \((-2, -6)\).