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

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

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

(−3, 6)

Answer 1

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

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

### Step 1: Align the equations
We have:
\[
4x - 6y = -48 \tag{1}
\]
\[
-2x + 4y = 30 \tag{2}
\]

### Step 2: Multiply the equations if necessary
We want to eliminate one of the variables. Let's eliminate \( x \) by making the coefficients of \( x \) the same. To do this, 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:
\[
-4x + 8y = 60 \tag{3}
\]

### Step 3: Add the equations
Now we can add equation (1) and the modified equation (3):
\[
(4x - 6y) + (-4x + 8y) = -48 + 60
\]
This simplifies to:
\[
2y = 12
\]
Now, divide both sides by \( 2 \):
\[
y = 6
\]

### Step 4: Substitute \( y \) back into one of the original equations to find \( x \)
We can substitute \( y = 6 \) back into the first equation:
\[
4x - 6(6) = -48
\]
This simplifies to:
\[
4x - 36 = -48
\]
Now, add \( 36 \) to both sides:
\[
4x = -48 + 36
\]
\[
4x = -12
\]
Now, divide by \( 4 \):
\[
x = -3
\]

### Solution
The solution to the system of equations is \( (x, y) = (-3, 6) \).

Thus, the correct answer is **(−3, 6)**.