Question

Choose the solutions of the following systems of equations x^2+y^2=6 and x^2-y=6

Answer 1

Answer:

The solutions are (-√6,0) and (√6,0)

(-√5,-1) and (√5,-1)

Step-by-step explanation:

The equations are:

${x}^{2} + {y}^{2} = 6$

and

${x}^{2} - y = 6$

We make y the subject in the second equation to get;

$y = {x}^{2} - 6$

We substitute into the first equation to get:

${x}^{2} + ({x}^{2} - 6 )^2= 6$

$x = \pm \sqrt{6}$

and $x = \pm \sqrt{5}$

The solutions are (-√6,0) and (√6,0)

(-√5,-1) and (√5,-1)