Solve the following system of equations using the elimination method.

3x−4y=−4 , x+3y=−10

(1 point)

1 answer

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:

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