Question

Solve the system y=x²-2 and x²+y=4.Illustrate graphically.

Answer 1

Solution:
`(-√(3),1),(√(3),1)`

Explanation:

System of equation:

`y=x^2-2\text{ and }x^2+y=4`

Using substitution method.

`y=x^2-2` substitute into
`x^2+y=4`

`x^2+x^2-2=4` (combine like term)

`2x^2=4+2` (Addition property of equality)

`2x^2=6` (division property of equality)

`x^2=3` (Taking square root)

`x=\pm √(3)`

Substitute x into
`y=x^2-2`

`y=(√(3))^2-2`

`y=1`

Solution:
`(-√(3),1),(√(3),1)`

Now cross check the solution using graph.

Please find attachment for graph.