Solve the system of two equations using elimination with multiplication.

4x - 6y = - 48

- 2x + 4y = 30 (1 point)

1 answer

To use the elimination method with multiplication for this system of equations, we need to manipulate the equations so that the coefficients of either the x or y terms will be the same or opposites.

First, let's multiply the second equation by 2 to make the coefficients of x the same.

2 * (- 2x + 4y) = 2 * 30

Simplifying this, we get -4x + 8y = 60.

Now we have the two equations:

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

By adding the two equations vertically, we can eliminate the x variable:

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

Simplifying this equation, we get:

-6y + 8y = 12

2y = 12

Dividing both sides by 2, we find:

y = 6

Now, we substitute this value of y back into either Equation 1 or Equation 2. Let's use Equation 1:

4x - 6(6) = - 48

Simplifying this equation, we get:

4x - 36 = -48

To isolate the x variable, we add 36 to both sides:

4x = -12

Dividing both sides by 4, we find:

x = -3

So the solution to the system of equations is x = -3 and y = 6.