How do you solve the system x+y=4 and x-y=2?

Mar 27, 2015

By adding the two equations together, the $y$ variable is reduced to $0$ leaving an equation with only the $x$ variable which is easy to solve.

$\left(x + y = 4\right)$
$+ \left(x - y = 2\right)$

$2 x = 6$ which implies $x = 3$

Substituting $x = 3$ back into the first equation
(3) + y = 4$\implies$y= 1#

The given equations intersect at $\left(x , y\right) = \left(3 , 1\right)$