Question

How do you solve `Y=2x^2-3` and `Y=3x-1`?

Answer 1

`(x,y) = (-1/2, -2 1/2) or (2,5)`

Explanation:

If
[1]`color(white)("XXX")y = 2x^2-3`
and
[2]`color(white)("XXX")y=3x-1`
then
[3]`color(white)("XXX")2x^2-3=3x-1`

Simplifying
[4]`color(white)("XXX")2x^2-3x-2=0`
Factoring
[5]`color(white)("XXX")(2x+1)(x-2)=0`

[6]`color(white)("XXX")x=-1/2color(white)("XXX")or [7]color(white)("XXX")x=2`

`{: (color(white)("XXX"),x=-1/2,color(white)("XXXXXXX"),x=2), (color(white)("XXX"),y=2x^2-3,color(white)("XXXXXXX"),y=2x^2-3), (color(white)("XXX"),color(white)("X")=1/2-3,color(white)("XXXXXXX"),color(white)("X")=8-3), (color(white)("XXX"),color(white)("X")=-2 1/2,color(white)("XXXXXXX"),color(white)("X")=5) :}`