Question

How do you solve the following system?: `-2x -5y =1, -x -y = -2`

Answer 1

Just like this. It is a big answer but it is easy to understand

Explanation:

First, put one line above the other:
`-2x -y = 1`
`-x-y=-2`

Now, we check if one line may delete(remainder = 0) any element from the other adding them:
`-2x+(-x) = -3x=>` No
`-y+(-y)=-2y=>` No
`1 +(-2) = -1 =>` No

Since add it has not deleted any element, multiply any of the lines by (-1) and try adding it again. I will chose the second line to multiply, its easier this way:
`-2x-y=1 ""=>` `-2x-y=1`
`-x-y=-2 =>` `x+y = 2`

Adding:
`-2x +x = -x =>` No
`-y+y = 0 =>` Yes!
`1 +2= 3=>` No

Since this way one element was deleted (`y`), we may put it all in one "universal line":
`-x + 0 = 3` that becomes `x = -3`

To find `y` its way more simple, you just put the value of `x` in any place that he belongs to. Again I will chose the second line, still easier.
`-(-3) - y = -2`
`-y+3 = -2`
`-y = -5`
`y = 5`