Solve the system of equations using elimanation
-2x+2y=6
4x+2y=-5

Your solution is (-11/6, 7/6).

Step-by-step explanation:

-2x + 2y = 6

4x + 2y = -5

Right away I can see that our y-values are the same. We want to eliminate one variable at a time, so let's make one of the 2y's a positive by multiplying each term in the equation by -1.

4x + 2y = -5

-1(4x + 2y = -5)

-4x - 2y = 5

Now we have a new equation in our system.

-2x + 2y = 6

-4x - 2y = 5

Now eliminate by performing each action given by the terms.

-2x + 2y = 6

-4x - 2y = 5

-6x = 11

Divide both sides by -6.

x = 11/-6

Now that we know x, plug it back into one of the original equations to find y.

-2x + 2y = 6

-2(11/-6) + 2y = 6

Multiply.

-22/-6 + 2y = 6

22/6 + 2y = 6

Subtract 22/6 from both sides.

2y = 6 - 22/6

2y = 36/6 - 22/6

2y = 14/6

2y = 7/3

Divide both sides by 2.

y = (7/3)/2

y = 7/6

Your solution is (-11/6, 7/6).

Check your answer by plugging both values into one of the original equations.

4x + 2y = -5

4(-11/6) + 2(7/6) = -5

Multiply.

-44/6 + 14/6 = -5

Add.

-30/6 = -5

Divide.

-5 = -5

Your answer is correct.

Hope this helps!

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