Question

What is the solution of -2x-2y=4 and x+5y=10

Answer 1

-2x - 2y = 4
x + 5y = 10

It looks like the method it would be easiest to use to solve this system is substitution. To use substitution, let us isolate x in the second equation:

x + 5y = 10
x = -5y + 10

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-2x - 2y = 4
-2(-5y + 10) - 2y = 4
10y - 20 - 2y = 4
8y - 20 = 4
8y = 24
y = 3

Now we can substitute back into the second equation to find x:

x + 5y = 10
x + 5(3) = 10
x + 15 = 10
x = -5

Finally, to check our work:

-2(-5) - 2(3) = 4   -->   10 - 6 = 4   <--True
-5 + 5(3) = 10   -->   -5 + 15 = 10   <--True

Answer:
y = 3
x = -5