Question

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

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

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

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

(−33,−9)

Answer 1

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

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

We want to eliminate one of the variables by making the coefficients of either \( x \) or \( y \) equal. Let's eliminate \( x \) first.

### Step 1: Multiply the equations
To eliminate \( x \), we can multiply the second equation by 2 so that the coefficients of \( x \) have the same absolute value.

Multiplying the second equation by 2:
\[
2(-2x + 4y) = 2(30)
\]
This gives us:
\[
-4x + 8y = 60
\]

### Step 2: Rewrite the equations
Now we rewrite the equations:
1) \( 4x - 6y = -48 \)
2) \( -4x + 8y = 60 \)

### Step 3: Add the equations
Next, we can add these two equations together to eliminate \( x \):
\[
(4x - 6y) + (-4x + 8y) = -48 + 60
\]
This simplifies to:
\[
0x + 2y = 12
\]
So we have:
\[
2y = 12
\]

### Step 4: Solve for \( y \)
Dividing both sides by 2:
\[
y = 6
\]

### Step 5: Substitute \( y \) back into one of the original equations
Now we can substitute \( y = 6 \) back into one of the original equations to find \( x \). We can use the first equation:
\[
4x - 6(6) = -48
\]
This simplifies to:
\[
4x - 36 = -48
\]
Adding 36 to both sides:
\[
4x = -12
\]
Dividing both sides by 4:
\[
x = -3
\]

### Final Solution
So, the solution to the system of equations is:
\[
(x, y) = (-3, 6)
\]

Checking the answer against the options provided:
The solution is \((-3, 6)\), which corresponds to the first option.

Thus, the correct answer is:
\[
\boxed{(-3, 6)}
\]