To solve the system of equations using the elimination method, we start with the given equations:
- \( 3x - 4y = -4 \)
- \( x + 3y = -10 \)
We can eliminate one of the variables by multiplying one or both of the equations. Let's eliminate \( x \).
First, we'll multiply the second equation by 3:
\[ 3(x + 3y) = 3(-10) \]
which simplifies to:
\[ 3x + 9y = -30 \quad (3) \]
Now we have the transformed system of equations:
- \( 3x - 4y = -4 \)
- \( 3x + 9y = -30 \)
Next, we'll subtract equation (1) from equation (3) to eliminate \( x \):
\[ (3x + 9y) - (3x - 4y) = -30 - (-4) \]
This simplifies to:
\[ 3x + 9y - 3x + 4y = -30 + 4 \] \[ 13y = -26 \]
Now, solve for \( y \):
\[ y = \frac{-26}{13} = -2 \]
Now that we have \( y = -2 \), we can substitute this value back into one of the original equations to find \( x \). We'll use equation (2):
\[ x + 3(-2) = -10 \] \[ x - 6 = -10 \] \[ x = -10 + 6 = -4 \]
Thus, the solution to the system of equations is:
\[ (x, y) = (-4, -2) \]
The correct response is:
\((−4,−2)\)