Question

Solve using elimination.
2x + y = 8
-2x - 2y = -18

Answer 1

Answer: x= -1 and y=10

How? Here=

Add the equations to eliminate x:

-y= -10

Then solve -y= -10 for y:

-y = -10

-y/-1 = -10/-1 (divide both sides by minus 1)

y=10

Now we have y we can plug it back in the equation and find out x.

2x - y = 8

2x - 10 = 8

2x + 10 + -10 = 8 + (-10)

(Add both sides with -10)

2x = -2

2x/2 = -2/2 (Divide both sides by 2)

x = -1

Answer: x=-1, y=10

Answer 2

To solve the system of equations using elimination we will eliminate one variable by adding the two equations together.

We have:

2x + y = 8 (Equation 1)

-2x - 2y = -18 (Equation 2)

To eliminate the x variable we can add Equation 1 and Equation 2 together:

(2x + y) + (-2x - 2y) = 8 + (-18)

2x - 2x + y - 2y = 8 - 18

- y = -10

Now we can solve for y by multiplying both sides of the equation by -1:

-1 * (-y) = -1 * (-10)

y = 10

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

2x + y = 8

2x + 10 = 8

Subtracting 10 from both sides:

2x = 8 - 10

2x = -2

Dividing both sides by 2:

x = -1

Therefore the solution to the system of equations is x = -1 and y = 10.