Question

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

Answer 1

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.

`(x+y=4)`
`+ (x-y=2)`

`2x =6` which implies `x=3`

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

The given equations intersect at `(x,y)=(3,1)`