Question

Solve the system using elimination.

2x + 6y = -12
5x - 5y = 10

Answer 1

(0,-2) x = 0 and y = -2.

Explanation:

Given system of equations:

2x + 6y = -12 (Equation 1)

5x - 5y = 10 (Equation 2)

To eliminate the variable "y," we need to multiply Equation 2 by 6 to make the coefficients of "y" in both equations equal.

6(5x - 5y) = 6(10)

30x - 30y = 60 (Equation 3)

Now, we have two equations:

2x + 6y = -12 (Equation 1)

30x - 30y = 60 (Equation 3)

Next, we'll multiply Equation 1 by -15 to make the coefficients of "x" in both equations equal.

-15(2x + 6y) = -15(-12)

-30x - 90y = 180 (Equation 4)

Now, we have two equations:

-30x - 90y = 180 (Equation 4)

30x - 30y = 60 (Equation 3)

By adding Equation 4 and Equation 3, we can eliminate "x":

(-30x - 90y) + (30x - 30y) = 180 + 60

-120y = 240

Dividing both sides of the equation by -120, we get:

y = -2

Now that we have the value of "y," we can substitute it back into one of the original equations to find the value of "x." Let's use Equation 1:

2x + 6(-2) = -12

2x - 12 = -12

Adding 12 to both sides of the equation:

2x = 0

Dividing both sides of the equation by 2, we get:

x = 0

Therefore, the solution to the system of equations is x = 0 and y = -2.

Answer 2

Solving the system of equations using elimination involves eliminating one variable by adding or subtracting the equations. Elimination method is as follows:

5(2x + 6y = -12)
2(5x - 5y = 10)

10x + 30y = -60
10x - 10y = 20

We subtract the equations eliminating the 10x term.
40y = -80
y = -2
x = (10 + (-2)5) / 5
x = 0