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Section 7.5 : Nonlinear Systems

Find the solution to each of the following system of equations.

1. \(\begin{align*}y & = - {x^2} + 5x + 16\\ y & = 7x - 8\end{align*}\)
2. \(\begin{align*}y & = 3 - {x^2}\\ y & = 8{x^2} + 2\end{align*}\)
3. \(\begin{align*}{x^2} + \frac{{{y^2}}}{4} & = 1\\ y & = 4 - 4x\end{align*}\)
4. \(\begin{align*}{x^2} + {y^2} & = 9\\ y & = 1 + \frac{{{x^2}}}{5}\end{align*}\)
5. \(\begin{align*}{x^2} + {y^2} & = 16\\ {y^2} - \frac{{{x^2}}}{{15}} & = 1\end{align*}\)
6. \(\begin{align*}xy & = - 2\\ {x^2} + \frac{{{y^2}}}{{25}} & = 1\end{align*}\)
7. \(\begin{align*}{x^2} + {y^2} & = 1\\ \frac{{{x^2}}}{4} + {y^2} & = 1\end{align*}\)
8. \(\begin{align*}{x^2} + {y^2} & = 3\\ \frac{{{x^2}}}{9} + {y^2} & = 1\end{align*}\)