Answer:
The solutions are (-√6,0) and (√6,0)
(-√5,-1) and (√5,-1)
Step-by-step explanation:
The equations are:
[tex] {x}^{2} + {y}^{2} = 6[/tex]
and
[tex] {x}^{2} - y = 6[/tex]
We make y the subject in the second equation to get;
[tex]y = {x}^{2} - 6[/tex]
We substitute into the first equation to get:
[tex] {x}^{2} + ({x}^{2} - 6 )^2= 6[/tex]
[tex]x = \pm \sqrt{6} [/tex]
and [tex]x = \pm \sqrt{5} [/tex]
The solutions are (-√6,0) and (√6,0)
(-√5,-1) and (√5,-1)
