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Solve the following system of equations using the elimination method.

3x−4y=−4, x+3y=−10

(1 point)
Responses

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

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

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

(−16,−2)

1 answer

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

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

First, we can manipulate one of the equations to align the terms for elimination. Let's solve Equation 2 for \(x\):

\[ x = -10 - 3y \]

Now we substitute \(x\) in Equation 1:

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

Distributing the \(3\):

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

Combine like terms:

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

Now, add \(30\) to both sides:

\[ -13y = 26 \]

Now, divide by \(-13\):

\[ y = -2 \]

Now that we have \(y\), substitute it back into the expression for \(x\):

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

Calculate:

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

So the solution to the system of equations is:

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

Therefore, the answer is:

\((−4,−2)\)