Question

How do you solve `x^2+y=8` and `x-2y=-6`?

Answer 1

`(-5/2, 7/2), (2, 4)`

Explanation:

`x^2+y=8`
`x-2y=-6`
In the first equation solve for y in terms of x:
`x^2+y=8` => `y=8-x^2`
Substitute for `y` in the second equation:
`x-2(8-x^2)=-6` => simplify:
`x-16+2x^2=-6` => add 6 to both sides and rewrite as:
`2x^2+x-10=0`
Solve by quadratic formula or by factoring,
`(2x+5)(x-2)=0`
`x=-5/2 or x=2`
Solve for y:
`y=8-(-5/2)^2 or y=8-2^2`
`y=8-25/4 or y=8-4`
`y=7/4 or y=4`
Hence the solutions are:
`(-5/2, 7/2), (2, 4)`