Question

Solve the following system of equations using the elimination method.

3x−4y=−4 , x+3y=−10

(1 point)

Answer 1

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

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

Let's eliminate \( x \) by manipulating these equations.

First, we can express \( x \) from the second equation:

\[
x = -10 - 3y
\]

Next, we will substitute this expression for \( x \) into the first equation:

\[
3(-10 - 3y) - 4y = -4
\]

Now, simplify this equation:

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

Combine like terms:

\[
-30 - 13y = -4
\]

Now, isolate \( y \):

\[
-13y = -4 + 30
\]
\[
-13y = 26
\]
\[
y = \frac{26}{-13} = -2
\]

Now that we have \( y \), we'll find \( x \) using the expression we had for \( x \):

\[
x = -10 - 3(-2) = -10 + 6 = -4
\]

So the solution to the system of equations is:

\[
(x, y) = (-4, -2)
\]

Thus, the solution is:

\[
\boxed{(-4, -2)}
\]