Question

How do you solve the system `x+y=12` and `x-y=2`?

Answer 1

`(7,5)`

Explanation:

Labelling the equation.

`xcolor(red)(+y)=12to(1)`

`xcolor(red)(-y)=2to(2)`

Note that adding + y and - y will eliminate them and leave an equation we can solve.

`"Adding "(1)+(2)"term by term gives"`

`(x+x)+(color(red)(+y-y))=(12+2)`

`rArr2x=14`

divide both sides by 2

`rArrx=7`

Substitute this value into either of the 2 equation, to find the corresponding value of y

`"Substituting in "(1)`

`7+y=12rArry=12-7`

`rArry=5`

`color(blue)"As a check"`

Substitute these values into both equations and if both sides are equal then they are the solution.

`"left side of "(1)to7+5=12to"true"`

`"left side of "(2)to7-5=2to"true"`

`rArr(7,5)" is the solution"`
graph{(y+x-12)(y-x+2)=0 [-11.1, 11.09, -5.55, 5.55]}