Question

Solve the system of two equations using elimination with multiplication.

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

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

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

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

(−21,−6)

Answer 1

[AI-generated answer — Bot GPT 3.5]

The correct answer is (3, 9).

Answer 2

[AI-generated answer — Step-by-Step Bot]

To solve the system of equations using elimination with multiplication, we will eliminate one of the variables through multiplication.

Let's start by multiplying the second equation by 2 to make the x-coefficients equal:

-2x + 4y = 30
2(-2x + 4y) = 2(30)
-4x + 8y = 60

Now, we can add this equation to the first equation:

4x - 6y + (-4x + 8y) = -48 + 60
-6y + 8y = 12
2y = 12
y = 6

Next, we will substitute the value of y into one of the original equations. Let's use the first equation:

4x - 6(6) = -48
4x - 36 = -48
4x = -48 + 36
4x = -12
x = -3

Therefore, the solution to the system of equations is (x, y) = (-3, 6).

Answer 3

[AI-generated answer — Explain Bot]

To solve the system of equations using elimination with multiplication, we need to eliminate one variable by multiplying the equations with appropriate constants, so that when they are added or subtracted, one variable cancels out.

Let's solve the system of equations step by step:

1. Multiply the second equation by 2 to eliminate the x variable:
-2x + 4y = 30
Multiply both sides by 2:
-4x + 8y = 60

2. Now, align the equations together:
4x − 6y = −48
-4x + 8y = 60

3. Add the two equations to eliminate the x variable:
(4x - 4x) + (-6y + 8y) = (-48 + 60)
2y = 12

4. Solve for y by dividing both sides of the equation by 2:
2y/2 = 12/2
y = 6

5. Substitute the value of y (6) back into one of the original equations, let's use the first equation:
4x - 6(6) = -48
4x - 36 = -48

6. Solve for x by adding 36 to both sides of the equation:
4x - 36 + 36 = -48 + 36
4x = -12

7. Divide both sides of the equation by 4 to solve for x:
(4x)/4 = (-12)/4
x = -3

So, the solution to the system of equations is (x, y) = (-3, 6).