To solve the system of equations using the elimination method, we have the following equations:
- \(3x - 4y = -4\) (Equation 1)
- \(x + 3y = -10\) (Equation 2)
First, we can manipulate one of the equations to align the terms for elimination. Let's solve Equation 2 for \(x\):
\[ x = -10 - 3y \]
Now we substitute \(x\) in Equation 1:
\[ 3(-10 - 3y) - 4y = -4 \]
Distributing the \(3\):
\[ -30 - 9y - 4y = -4 \]
Combine like terms:
\[ -30 - 13y = -4 \]
Now, add \(30\) to both sides:
\[ -13y = 26 \]
Now, divide by \(-13\):
\[ y = -2 \]
Now that we have \(y\), substitute it back into the expression for \(x\):
\[ x = -10 - 3(-2) \]
Calculate:
\[ x = -10 + 6 = -4 \]
So the solution to the system of equations is:
\[ (x, y) = (-4, -2) \]
Therefore, the answer is:
\((−4,−2)\)