1 month ago

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

Mathematics

1 answer:

AnnZ [12.3K]1 month ago

7 0

Answer:

The solutions are (-√6,0) and (√6,0)

(-√5,-1) and (√5,-1)

Step-by-step explanation:

We start with the equations:

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

and

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

Rearranging the second equation to make y the subject results in;

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

Substituting into the first equation gives us:

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

$x = \pm \sqrt{6}$

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

The solutions remain as (-√6,0) and (√6,0)

(-√5,-1) and (√5,-1)

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