Question

How do you solve `y=|x|` and `y=1/2x+4` using substitution?

Answer 1

`(x,y)=(8,8)` or `(x,y)=(-8/3,8/3)`

Explanation:

Given
[1]`color(white)("XXX")y=abs(x)`
[2]`color(white)("XXX")y=1/2x+4`

Substituting `abs(x)` for `y` (based on [1])
in [2], we get:
[3]`color(white)("XXX")abs(x)=1/2x+4`

which implies:
`{: ("either ",[4]color(white)("xx")-x=1/2x+4," or ",[8]color(white)("xx")x=1/2x+4), (,rarr[5]color(white)("xx")-3/2x=4,,rarr[9]color(white)("xx")1/2x=4), (,rarr[6]color(white)("xx")x=-8/3,,rarr[10]color(white)("xx")x=8), ("then based on [1]",,,), (,rarr[7]color(white)("xx")y=8," or ",rarr[11]color(white)("xx")y=8/3) :}`