# How do you solve x+y=-1 and x-y=3?

Nov 4, 2015

color(green)(x = 1
color(green)(y = -2

#### Explanation:

$x + y = - 1$ -------(1)
$x - y = 3$ -------(2)

By asking us to solve, the question is indirectly asking us for the value of $x \mathmr{and} y$

To get the value of $x$, let's ADD the two equations. Because ADDING will help us eliminate $y$ with ease.

$\left(x + y\right) + \left(x - y\right) = - 1 + 3$

$x + \cancel{y} + x - \cancel{y} = 2$

$2 x = 2$

Dividing both sides by 2, we get

$\frac{\cancel{2} x}{\cancel{2}} = \frac{2}{2}$

color(green)(x = 1

Now to get the value of $y$ can simply substitute this value of $x$ in any of the two equations

Substituting $x = 1$ in the first equation, we get

$1 + y = - 1$

Transposing 1 to the right hand side, we get

$y = - 1 - 1$

color(green)(y = -2