Solve the following system of equations using the elimination method.

Question

3x−4y=−4
, x+3y=−10


(1 point)
Responses

(−4,−2)
left parenthesis negative 4 comma negative 2 right parenthesis

(−16,2)
left parenthesis negative 16 comma 2 right parenthesis

(−2,−4)
left parenthesis negative 2 comma negative 4 right parenthesis

(−16,−2)

Answer 1

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

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

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

First, let's manipulate Equation 2 to eliminate \( x \).

We can express \( x \) in terms of \( y \) from Equation 2:

\[ x = -10 - 3y \]

Now, substitute this expression for \( x \) into Equation 1:

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

Expanding this gives:

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

Combine like terms:

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

Now, add 30 to both sides:

\[ -13y = 26 \]

Dividing both sides by -13 gives:

\[ y = -2 \]

Now, substitute \( y = -2 \) back into the equation we derived for \( x \):

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

Calculating \( x \):

\[ x = -10 + 6 = -4 \]

Thus, the solution is

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

From the provided options, the correct answer is:

(−4,−2)