Solving Simultaneous Equations Using Elimination Quick Check

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

1. \( 3x - 4y = -4 \) (Equation 1)
2. \( x + 3y = -10 \) (Equation 2)

We can start by eliminating one of the variables. Let's eliminate \( x \). To do this, we can multiply Equation 2 by 3 so that the coefficients of \( x \) in both equations will be the same.

Multiply Equation 2 by 3:

\[
3(x + 3y) = 3(-10)
\]

This gives:

\[
3x + 9y = -30 \quad \text{(Equation 3)}
\]

Now we can set Equation 1 and Equation 3 up for elimination:

1. \( 3x - 4y = -4 \) (Equation 1)
2. \( 3x + 9y = -30 \) (Equation 3)

Next, we subtract Equation 1 from Equation 3:

\[
(3x + 9y) - (3x - 4y) = -30 - (-4)
\]

This simplifies to:

\[
9y + 4y = -30 + 4
\]

\[
13y = -26
\]

Now, divide by 13:

\[
y = -2
\]

Now that we have \( y \), we can substitute it back into Equation 2 to solve for \( x \):

\[
x + 3y = -10
\]

Substituting \( y = -2 \):

\[
x + 3(-2) = -10
\]

\[
x - 6 = -10
\]

Adding 6 to both sides:

\[
x = -4
\]

The solution to the system of equations is \( (x, y) = (-4, -2) \).

So the correct answer is:

**(−4,−2)**