91Ó°ÊÓ

Solve each nonlinear system of equations analytically for all real solutions. $$\begin{aligned} &x^{2}+3 x y+y^{2}=5\\\ &x^{2}-2 x y-y^{2}=-7 \end{aligned}$$

Use substitution to solve the nonlinear system of equations in three variables. Note that solutions are ondered triples. $$\begin{aligned} 2 x^{2}+y^{2}+3 z^{2} &=3 \\ 2 x+y-z &=1 \\ x+y &=0 \end{aligned}$$

Write an equation for each parabola with vertex at the origin. Through \((2,-2 \sqrt{2}) ;\) opening to the right

Write the equation in standard form for a hyperbola centered at ( \(h, k\) ). Identify the center and vertices. $$3 y^{2}+24 y-2 x^{2}+12 x+24=0$$

Use substitution to solve the nonlinear system of equations in three variables. Note that solutions are ondered triples. $$\begin{aligned} &x^{2}+y^{2}+z^{2}=4\\\ &x+y+z=2\\\ &x-y \quad=0 \end{aligned}$$

Write the equation in standard form for a hyperbola centered at ( \(h, k\) ). Identify the center and vertices. $$4 x^{2}+16 x-9 y^{2}+18 y=29$$

Write an equation for each parabola with vertex at the origin. Through \((\sqrt{3}, 3) ;\) opening upward

Write an equation for each parabola with vertex at the origin. Through \((\sqrt{10},-5) ;\) opening downward

Write the equation in standard form for a hyperbola centered at ( \(h, k\) ). Identify the center and vertices. $$x^{2}-6 x-2 y^{2}+7=0$$

Use substitution to solve the nonlinear system of equations in three variables. Note that solutions are ondered triples. $$\begin{aligned} &\frac{x^{2}}{16}+\frac{y^{2}}{4} \leq 1\\\ &x^{2}-y^{2} \geq 1 \end{aligned}$$