Question

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

Answer 1

`(x,y)to(3,-1)`

Explanation:

`y=-x+2to(1)`

`y=x-4to(2)`

`"adding "(1)" and "(2)" will eliminate term in x"`

`"adding term by term on both sides"`

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

`rArr2y=-2`

`"divide both sides by 2"`

`(cancel(2) y)/cancel(2)=(-2)/2`

`rArry=-1`

`"substitute this value into either equation "(1)" or "(2)`

`"substituting in equation "(2)" gives"`

`-1=x-4rArrx=-1+4=3`

`"point of intersection "=(3,-1)`
graph{(y+x-2)(y-x+4)((x-3)^2+(y+1)^2-0.04)=0 [-10, 10, -5, 5]}