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 start with the following equations:

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

Step 1: Align equations

We will eliminate one variable by aligning the equations. Let's express them in a suitable form for elimination.

Multiply Equation 2 by 3 to align with the coefficient of \(x\) in Equation 1:

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

This gives us:

\[ 3x + 9y = -30 \quad \text{(Equation 3)} \]

Step 2: Set up for elimination

Now, we have:

1. \( 3x - 4y = -4 \) (Equation 1)
2. \( 3x + 9y = -30 \) (Equation 3)

Step 3: Eliminate \(x\)

Subtract Equation 1 from Equation 3:

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

This simplifies to:

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

Combining like terms:

\[ 13y = -26 \]

Step 4: Solve for \(y\)

Now, divide by 13:

\[ y = -2 \]

Step 5: Substitute \(y\) back to solve for \(x\)

Substituting \(y = -2\) back into Equation 2:

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

Final Solution

The solution to the system of equations is \( (x, y) = (-4, -2) \).

Thus, the correct answer is:

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