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Find the $x$ and $y$ values that satisfy both of the following equations. That is, find the point of intersection of the two curves.

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
$y$$=$$\\simplify{{ak}/({b}x)}$               $(1)$
$y$$=$$\\simplify{{a}x^2/{b}}$               $(2)$
\n

$x=$ [[0]],   $y=$ [[1]]

\n

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Given

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
$y$$=$$\\simplify{{ak}/({b}x)}$               $(1)$
$y$$=$$\\simplify{{a}x^2/{b}}$               $(2)$
\n

substitute the expression for $y$ given in $(1)$ into $(2)$:
\\[\\simplify{{ak}/({b}x) ={a}x^2/{b}}\\]

\n

To get rid of the $x$ in the denominator, let us multiply both sides by $x$
\\[\\simplify{{ak}/({b}) ={a}x^3/{b}}\\]

\n

Since there is only one term with an $x$ in it, we can get $x^3$ by itself

\n

\\[x^3=\\var{cubed}\\]

\n

Therefore, $x=\\sqrt[3]{\\var{cubed}}=\\var{xans}$.

\n


Now we know the $x$ value we can determine the corresponding $y$ value by substituting $x=\\var{xans}$ into either equation $(1)$ or $(2)$, below we substitute into $(2)$:

\n\n\n\n\n\n\n\n\n\n\n\n\n\n
\n

$y$

\n		\n

$=$

\n		\n

$\\simplify{{a}/{b}}(\\var{xans})^2$

\n
\n

$=$

\n		\n

$\\simplify[fractionnumbers]{{a*xans^2/b}}$

\n
\n

Therefore the values that satisfy equations $(1)$ and $(2)$ are $x=\\var{xans}$ and $y=\\simplify[fractionnumbers]{{a*xans^2/b}}$.

\n

 

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