How do you find the exact solutions to the system $y=5$ and $y^2=x^2+9$ ?

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Answer 1 · 2017-01-21T13:58:57

$y = 5$
$x=+-4$

First substitute $y=5$ into $y^2=x^2+9$

You get: $5^2 = x^2 +9$

Square the 5 and take 9 away from both sides: $25-9=x^2$

Simplify: $16=x^2$
Therefore $x=+-sqrt(16)$
So $x=+-4$

You already know that $y = 5$ and now you know that $x=+-4$

(Techincally $y = +-5$ as $5^2=25$ and $(-5)^2 = 25$ which are the same answers.)

How do you find the exact solutions to the system y=5y=5 and y^2=x^2+9y^2=x^2+9?