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:

\((-4, -2)\)