Question

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Solving with Elimination Quick Check
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Question
Solve the system of two equations using elimination with multiplication.
4x−6y=−48

−2x+4y=30
(1 point)
Responses

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

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

(−21,−6)
left parenthesis negative 21 comma negative 6 right parenthesis

(−3, 6)

Answer 1

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

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

First, we can manipulate the equations to align them for elimination. To do this, let's multiply the second equation by 2 to make the coefficients of \(x\) match (but opposite in sign):

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

This simplifies to:

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

Now our system of equations looks like this:

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

Now we can add both equations together:

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

This simplifies to:

\[
0x + 2y = 12
\]

Now, solving for \(y\):

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

Next, we substitute \(y = 6\) back into one of the original equations to find \(x\). We'll use the first equation:

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

This simplifies to:

\[
4x - 36 = -48 \\
4x = -48 + 36 \\
4x = -12 \\
x = -3
\]

Thus, the solution to the system is:

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

So, the correct answer from the provided options is:

\((-3, 6)\)