Question

Solve the system of two equations using elimination with multiplication. 4x−6y=−48 −2x+4y=30 (1 point)

(−21,−6) left parenthesis negative 21 comma negative 6 right parenthesis (−3, 6) left parenthesis negative 3 comma 6 right parenthesis (3, 9) left parenthesis 3 comma 9 right parenthesis (−33,−9)

Answer 1

To solve the system of equations using elimination, we have the following two equations:

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

First, we can modify Equation 2 to align the coefficients of \(x\) when we eliminate the variable \(x\). We can multiply Equation 2 by 2 to make the coefficient of \(x\) match the coefficient of \(x\) in Equation 1.

Multiplying Equation 2 by 2:

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

This gives us:

\[
-4x + 8y = 60 \quad \text{(Equation 3)}
\]

Now we have:

1. \( 4x - 6y = -48 \) (Equation 1)
2. \( -4x + 8y = 60 \) (Equation 3)

Next, we can add Equation 1 and Equation 3 together to eliminate \(x\):

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

This simplifies to:

\[
0x + 2y = 12
\]

Thus, we have:

\[
2y = 12
\]

Dividing both sides by 2 gives:

\[
y = 6
\]

Now that we have the value of \(y\), we can substitute it back into one of the original equations to solve for \(x\). We can use Equation 1:

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

Calculating this, we have:

\[
4x - 36 = -48
\]

Adding 36 to both sides:

\[
4x = -12
\]

Dividing both sides by 4 gives:

\[
x = -3
\]

Thus, the solution to the system of equations is:

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

The answer is:

\[
\boxed{(-3, 6)}
\]