Question

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
(−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:

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