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

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

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

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

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

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

Step 1: Align the equations for elimination.

We can multiply Equation 2 by 3 so that the coefficient of \(x\) in both equations will match. This will allow us to eliminate \(x\) when we subtract the two equations:

\[ 3(x + 3y) = 3(-10) \] \[ 3x + 9y = -30 (Equation 3) \]

Now we have:

\(3x - 4y = -4\) (Equation 1)
\(3x + 9y = -30\) (Equation 3)

Step 2: Subtract Equation 1 from Equation 3 to eliminate \(x\):

Now subtract Equation 1 from Equation 3:

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

This simplifies to:

\[ 3x + 9y - 3x + 4y = -30 + 4 \] \[ 13y = -26 \]

Now solve for \(y\):

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

Step 3: Substitute \(y\) back into one of the original equations to find \(x\):

We can substitute \(y = -2\) back into Equation 2:

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

Step 4: Write the solution as an ordered pair:

The solution to the system of equations is:

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

Thus, the answer is:

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