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

Apr 13, 2016

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

#### Explanation:

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

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

$- 2 x + x = - x \implies$ No
$- y + y = 0 \implies$ Yes!
$1 + 2 = 3 \implies$ 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.
$- \left(- 3\right) - y = - 2$
$- y + 3 = - 2$
$- y = - 5$
$y = 5$