Solve the system of two equations using elimination with multiplication.

Question

4x−6y=−48
−2x+4y=30(1 point)
Responses

(−3, 6)
left parenthesis negative 3 comma 6 right parenthesis

(−33,−9)
left parenthesis negative 33 comma negative 9 right parenthesis

(3, 9)
left parenthesis 3 comma 9 right parenthesis

(−21,−6

Answer 1

To solve the system of equations using elimination with multiplication, we have the equations:

1. \( 4x - 6y = -48 \)
2. \( -2x + 4y = 30 \)

We can manipulate these equations to eliminate one of the variables. Let's eliminate \(x\) by making the coefficients of \(x\) the same in both equations.

We can multiply the second equation by 2 to match the coefficient of \(x\) in the first equation:

\[ 2(-2x + 4y) = 2(30) \]

This gives us:

\[ -4x + 8y = 60 \]

Now we can rewrite our system of equations:

1. \( 4x - 6y = -48 \)
2. \( -4x + 8y = 60 \)

Next, we can add these two equations together to eliminate \(x\):

\[ (4x - 6y) + (-4x + 8y) = -48 + 60 \]

This simplifies to:

\[ 0 + 2y = 12 \]

We can solve for \(y\):

\[ 2y = 12 \ y = 6 \]

Now that we have \(y\), we can substitute it back into one of the original equations to solve for \(x\). We'll use the first equation:

\[ 4x - 6(6) = -48 \ 4x - 36 = -48 \]

Now we add 36 to both sides:

\[ 4x = -48 + 36 \ 4x = -12 \]

Dividing both sides by 4 gives:

\[ x = -3 \]

Thus, the solution to the system of equations is:

\[ (x, y) = (-3, 6) \]

The correct answer is:

\((−3, 6)\)