Question

Quais são as funções do sistema de equação 3y = 2x + 6 e 4x² +9y²=36

Answer 1

3y = 2x + 6

$y \ = \frac{2x \ + \ 6}{3}$

$y \ = \frac{2x}{3} \ + \ \frac{6}{3}$

$y \ = \frac{2x}{3} \ + \ 2$

$\boxed{\bold{f(x) \ = \frac{2x}{3} \ + \ 2 }}$


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4x² + 9y² = 36

$9y^2 \ = \ 36 \ - \ 4x^2$

$y^2 \ = \frac{-4x^2 \ + \ 36}{9}$

$y^2 \ = -\frac{4x^2}{9} \ + \ \frac{36}{9}$

$y^2 \ = -\frac{4x^2}{9} \ + \ 4$

$y \ = \sqrt{-\frac{4x^2}{9} \ + \ 4 }$

$\boxed{\bold{f(x) \ = \sqrt{-\frac{4x^2}{9} \ + \ 4 }}}$


Ou ainda:


$9y^2 \ = \ 36 \ - \ 4x^2$

$y^2 \ = \frac{-4x^2 \ + \ 36}{9}$

$y \ = \sqrt{\frac{-4x^2 \ + \ 36}{9}}$

$y \ = \frac{\sqrt{-4x^2 \ + \ 36}}{\sqrt{9}}$

$y \ = \frac{\sqrt{-4x^2 \ + \ 36}}{3}$

$\larged{\boxed{\bold{f(x) \ = \frac{\sqrt{-4x^2 \ + \ 36}}{3}}}}$