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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$\\simplify{{a*xans^2/b}}$\n
\n

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

\n

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