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Solve the following system of equations using the elimination method.

3x−4y=−4 , x+3y=−10

(1 point)
Responses

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

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

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

(−16,−2)

1 answer

To solve the system of equations using the elimination method, we start with the given equations:

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

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

First, we will multiply the second equation to align the coefficients of \(x\) or \(y\). We can multiply the second equation by 3:

\[ 3(x + 3y) = 3(-10) \] This gives us:

\[ 3x + 9y = -30 \]

Now, we have the following system of equations:

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

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

Next, we will subtract the first equation from the second equation to eliminate \(3x\):

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

This simplifies to:

\[ 9y + 4y = -30 + 4 \] \[ 13y = -26 \] \[ y = -2 \]

Now that we have \(y\), we can substitute it back into one of the original equations to find \(x\). We'll use the second equation:

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

Thus, the solution to the system of equations is:

\((x, y) = (-4, -2)\).

The answer is:

\(\boxed{(-4, -2)}\).