# How do you solve the following system of equations?: x+y= -2 , x-2y=13?

Mar 23, 2018

$x = 3$
$y = - 5$

#### Explanation:

since we have two unknowns we need minimum of two equations to solve for them , and we have that too

lets see the first equation
$x + y = - 2$
the first objective is to write either x in terms of y or y in terms of x
so i add -y to both sides , and we get
$x = - 2 - y$
take this value of x and plug it in equation 2
so
this $x - 2 y = 13$
becomes
$\left(- 2 - y\right) - 2 y = 13$
solve for y to get a value
$- 2 - 3 y = 13$
$- 3 y = 15$
$- y = 5$
or
$y = - 5$
since we got y value , we can plug it back in the first equation to get x value
$x + \left(- 5\right) = - 2$ or $x = 5 - 2 = 3$
So , $x = 3 , y = - 5$

Mar 23, 2018

$x = 3$
$y = - 5$

#### Explanation:

You add/subtract the two equations with each other, using the $=$ sign as a point of reference:

$x + y = - 2$

would be the first equation. We can label it as equation $\left(1\right)$

$x - 2 y = 13$

would be the second equation. We can label it as equation $\left(2\right)$

Now, we can subtract equation $\left(2\right)$ from equation $\left(1\right)$ [the idea here is to leave us with only one variable, that way we can solve the equation as usual]

$\left(1\right) - \left(2\right)$ would be

$x - x + y - \left(- 2 y\right) = - 2 - 13$

$0 + 3 y = - 15$

so

$y = - 5$

Now we can take $y$ and use it in equation $\left(1\right)$;

$x + \left(- 5\right) = - 2$

$x = 3$

So

$x = 3 \mathmr{and} y = - 5$