Question

Solve the following system of equations using the elimination method.%0D%0A%0D%0A3x−4y=−4 , x+3y=−10 %0D%0A%0D%0A(1 point)%0D%0AResponses%0D%0A%0D%0A(−16,−2)%0D%0Aleft parenthesis negative 16 comma negative 2 right parenthesis%0D%0A%0D%0A(−4,−2)%0D%0Aleft parenthesis negative 4 comma negative 2 right parenthesis%0D%0A%0D%0A(−16,2)%0D%0Aleft parenthesis negative 16 comma 2 right parenthesis%0D%0A%0D%0A(−2,−4

Answer 1

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

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

### Step 1: Eliminate one variable
We will eliminate \(x\). To do this, we can multiply the second equation by 3 to align the coefficients of \(x\):

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

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

### Step 2: Write the new system of equations
Now we have the following system:

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

### Step 3: Subtract the first equation from the second
Now we subtract the first equation from the second:

\[
(3x + 9y) - (3x - 4y) = -30 - (-4)
\]
This simplifies to:

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

### Step 4: Solve for \(y\)
Dividing both sides by 13 gives:

\[
y = -2
\]

### Step 5: Substitute back to find \(x\)
Now we substitute \(y = -2\) back into one of the original equations. We'll use the second equation:

\[
x + 3(-2) = -10
\]
This simplifies to:

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

### Final Solution
The solution to the system of equations is:

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

Thus, the correct answer is:

\((-4, -2)\)