Question

`x+y=10" " and x-y=2` What is `x?`

Answer 1

`x=6,y=4`

Explanation:

`|(x+y=10),(x-y=2)|`
Add both equations together.
`x+x+y-y=10+2`
`2x=12|:2`
`x=6`
Sub the result into any of the two equations for `x`
`6+y=10|-6`
`y=4`

Answer 2

`x = 6`
`y = 4`

Explanation:

Given
`x+y=10`
`x-y=  2`
Solve for `x`

This is a Simultaneous Equations problem.

Add the equations to let `y` drop out as zero

`color(white)(m)` `x+y=10`
`color(white)(m)` `x-y=   2`
`color(white)()`―――――――
`2x   color(lightgray) (+ 0) =  12`
`color(white)(n)` `xcolor(white)(mnn)=   6` `larr` answer

If `x` equals `6`, then `y` must equal `4`

`color(white)(mmmmmm)`―――――――

Check

Sub in the values in the place of the letters to verify that the equations are still correct.

`color(white)(m)` `x+y=10`
`color(white)(m)` `6+4=10`  ✓

`color(white)(m)` `x-y=2`
`color(white)(m)` `6-4=2`  ✓

`Check`