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

Aug 1, 2015

Add the two equations together to get $2 x = 4$ hence $x = 2$
Subtract the two equations to get $2 y = 2$ hence $y = 1$

#### Explanation:

Add the two equations to find:

$2 x = \left(x + \textcolor{red}{\cancel{\textcolor{b l a c k}{y}}}\right) + \left(x - \textcolor{red}{\cancel{\textcolor{b l a c k}{y}}}\right) = 3 + 1 = 4$

Divide both ends by $2$ to get $x = 2$

Subtract the two equations to find:

$2 y = \left(\textcolor{red}{\cancel{\textcolor{b l a c k}{x}}} + y\right) - \left(\textcolor{red}{\cancel{\textcolor{b l a c k}{x}}} - y\right) = 3 - 1 = 2$

Divide both ends by $2$ to get $y = 1$