Nonlinear Systems of Equations in Two Variables

$\rhd$ Nonlinear systems of equations I (5:44) Solve the system of equations by graphing. Check your solution algebraically.
${\begin{cases} y = x^{2} + 6 \\ y = - 2 x - 2 \end{cases}$
Solutions: $(- 2, 2)$ and $(4, - 10)$
$\rhd$ Systems of nonlinear equations II (3:33) Find the solution(s) of
${\begin{cases} y = \frac{1}{2} x \\ 2 x^{2} - y^{2} = 7 \end{cases}$ . Solutions: $x = 2$ or $x = - 2$ giving points $(2, 1)$ and $(- 2, - 1)$ , both of which satisfy both constraint equations.
$\rhd$ Systems of nonlinear equations III (4:13)
Find the solution(s) of the system of equations
${\begin{cases} y = x + 1 \\ x^{2} + y^{2} = 25 \end{cases}$ Solutions: $(- 4, - 3)$ and $(4, 3)$
There are also more videos under “Quadratics” — see Systems of Quadratic Equations

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Nonlinear Systems of Equations in Two Variables

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