91Ó°ÊÓ

Solve each system using the elimination method or a combination of the elimination and substitution methods. $$ \begin{array}{l} 3 x^{2}+2 x y-3 y^{2}=5 \\ -x^{2}-3 x y+y^{2}=3 \end{array} $$

Graph each ellipse. $$\frac{x^{2}}{36}+\frac{y^{2}}{16}=1$$

Graph each ellipse. $$\frac{x^{2}}{9}+\frac{y^{2}}{4}=1$$

Solve each system using the elimination method or a combination of the elimination and substitution methods. $$ \begin{array}{r} -2 x^{2}+7 x y-3 y^{2}=4 \\ 2 x^{2}-3 x y+3 y^{2}=4 \end{array} $$

Solve each problem using a nonlinear system. The area of a rectangular rug is \(84 \mathrm{ft}^{2}\) and its perimeter is \(38 \mathrm{ft}\). Find the length and width of the rug.

Graph each ellipse. $$\frac{x^{2}}{16}+\frac{y^{2}}{4}=1$$

Solve each problem using a nonlinear system. Find the length and width of a rectangular room whose perimeter is \(50 \mathrm{~m}\) and whose area is \(100 \mathrm{~m}^{2}\).

Graph each ellipse. $$\frac{x^{2}}{49}+\frac{y^{2}}{81}=1$$

Solve each problem using a nonlinear system. A company has found that the price \(p\) (in dollars) of its scientific calculator is related to the supply \(x\) (in thousands) by the equation $$ p x=16 $$ The price is related to the demand \(x\) (in thousands) for the calculator by the equation $$ p=10 x+12 $$ The equilibrium price is the value of \(p\) where demand equals supply. Find the equilibrium price and the supply/demand at that price. (Hint: Demand, price, and supply must all be positive.)

Graph each ellipse. $$\frac{y^{2}}{25}=1-\frac{x^{2}}{49}$$