Chapter 10

Solve each nonlinear system of equations for real solutions. $$ \left\\{\begin{aligned} x^{2}+y^{2} &=25 \\ 4 x+3 y &=0 \end{aligned}\right. $$

The graph of each equation is a parabola. Determine whether the parabola opens upward, downward, to the left, or to the right. Do not graph. $$y=x^{2}-7 x+5$$

Identify the graph of each equation as an ellipse or a hyperbola. Do not graph. \(\frac{x^{2}}{16}+\frac{y^{2}}{4}=1\)

Solve each nonlinear system of equations for real solutions. $$ \left\\{\begin{aligned} x^{2}+y^{2} &=25 \\ 3 x+4 y &=0 \end{aligned}\right. $$

Graph each inequality. See Examples 1 and \(2 .\) $$ y<-x^{2} $$

The graph of each equation is a parabola. Determine whether the parabola opens upward, downward, to the left, or to the right. Do not graph. $$y=-x^{2}+16$$

Identify the graph of each equation as an ellipse or a hyperbola. Do not graph. \(\frac{x^{2}}{16}-\frac{y^{2}}{4}=1\)

Solve each nonlinear system of equations for real solutions. $$ \left\\{\begin{aligned} x^{2}+4 y^{2} &=10 \\ y &=x \end{aligned}\right. $$

Graph each inequality. See Examples 1 and \(2 .\) $$ x^{2}+y^{2} \geq 16 $$

The graph of each equation is a parabola. Determine whether the parabola opens upward, downward, to the left, or to the right. Do not graph. $$x=-y^{2}-y+2$$

Identify the graph of each equation as an ellipse or a hyperbola. Do not graph. \(x^{2}-5 y^{2}=3\)

Solve each nonlinear system of equations for real solutions. $$ \left\\{\begin{aligned} 4 x^{2}+y^{2} &=10 \\ y &=x \end{aligned}\right. $$

The graph of each equation is a parabola. Determine whether the parabola opens upward, downward, to the left, or to the right. Do not graph. $$x=3 y^{2}+2 y-5$$

Identify the graph of each equation as an ellipse or a hyperbola. Do not graph. \(-x^{2}+5 y^{2}=3\)

Graph each inequality. See Examples 1 and \(2 .\) $$ x^{2}+y^{2}<36 $$

Solve each nonlinear system of equations for real solutions. $$ \left\\{\begin{aligned} y^{2} &=4-x \\ x-2 y &=4 \end{aligned}\right. $$

Identify the graph of each equation as an ellipse or a hyperbola. Do not graph. \(-\frac{y^{2}}{25}+\frac{x^{2}}{36}=1\)

The graph of each equation is a parabola. Determine whether the parabola opens upward, downward, to the left, or to the right. Do not graph. $$y=-x^{2}+2 x+1$$

Solve each nonlinear system of equations for real solutions. $$ \left\\{\begin{array}{l} {x^{2}+y^{2}=4} \\ {x+y=-2} \end{array}\right. $$

Identify the graph of each equation as an ellipse or a hyperbola. Do not graph. \(\frac{y^{2}}{25}+\frac{x^{2}}{36}=1\)

The graph of each equation is a parabola. Determine whether the parabola opens upward, downward, to the left, or to the right. Do not graph. $$x=-y^{2}+2 y-6$$

Graph each inequality. See Examples 1 and \(2 .\) $$ x^{2}-\frac{y^{2}}{9} \geq 1 $$

Solve each nonlinear system of equations for real solutions. $$ \left\\{\begin{array}{r} {x^{2}+y^{2}=9} \\ {16 x^{2}-4 y^{2}=64} \end{array}\right. $$

Sketch the graph of each equation. \(\frac{x^{2}}{4}+\frac{y^{2}}{25}=1\)

The graph of each equation is a parabola. Find the vertex of the parabola and then graph it. $$x=3 y^{2}$$

Graph each inequality. See Examples 1 and \(2 .\) $$ y>(x-1)^{2}-3 $$

Solve each nonlinear system of equations for real solutions. $$ \left\\{\begin{array}{l} {4 x^{2}+3 y^{2}=35} \\ {5 x^{2}+2 y^{2}=42} \end{array}\right. $$

Sketch the graph of each equation. \(\frac{x^{2}}{16}+\frac{y^{2}}{9}=1\)

The graph of each equation is a parabola. Find the vertex of the parabola and then graph it. $$x=5 y^{2}$$

Solve each nonlinear system of equations for real solutions. $$ \left\\{\begin{array}{l} {x^{2}+2 y^{2}=2} \\ {x-y=2} \end{array}\right. $$

Sketch the graph of each equation. \(\frac{x^{2}}{9}+y^{2}=1\)

The graph of each equation is a parabola. Find the vertex of the parabola and then graph it. $$x=-2 y^{2}$$

Solve each nonlinear system of equations for real solutions. $$ \left\\{\begin{array}{l} {x^{2}+2 y^{2}=2} \\ {x^{2}-2 y^{2}=6} \end{array}\right. $$

Sketch the graph of each equation. \(x^{2}+\frac{y^{2}}{4}=1\)

The graph of each equation is a parabola. Find the vertex of the parabola and then graph it. $$x=-4 y^{2}$$

Solve each nonlinear system of equations for real solutions. $$ \left\\{\begin{aligned} y &=x^{2}-3 \\ 4 x-y &=6 \end{aligned}\right. $$

Sketch the graph of each equation. \(9 x^{2}+y^{2}=36\)

The graph of each equation is a parabola. Find the vertex of the parabola and then graph it. $$y=-4 x^{2}$$

Graph each inequality. See Examples 1 and \(2 .\) $$ y>-x^{2}+5 $$

Solve each nonlinear system of equations for real solutions. $$ \left\\{\begin{aligned} y &=x+1 \\ x^{2}-y^{2} &=1 \end{aligned}\right. $$

Sketch the graph of each equation. \(x^{2}+4 y^{2}=16\)

The graph of each equation is a parabola. Find the vertex of the parabola and then graph it. $$y=-2 x^{2}$$

Solve each nonlinear system of equations for real solutions. $$ \left\\{\begin{aligned} y &=x^{2} \\ 3 x+y &=10 \end{aligned}\right. $$

Graph each inequality. See Examples 1 and \(2 .\) $$ \frac{x^{2}}{4}+\frac{y^{2}}{9} \leq 1 $$

Sketch the graph of each equation. \(4 x^{2}+25 y^{2}=100\)

The graph of each equation is a parabola. Find the vertex of the parabola and then graph it. $$x=(y-2)^{2}+3$$

Solve each nonlinear system of equations for real solutions. $$ \left\\{\begin{array}{r} {6 x-y=5} \\ {x y=1} \end{array}\right. $$

Graph each inequality. See Examples 1 and \(2 .\) $$ \frac{x^{2}}{25}+\frac{y^{2}}{4} \geq 1 $$

Sketch the graph of each equation. \(36 x^{2}+y^{2}=36\)

The graph of each equation is a parabola. Find the vertex of the parabola and then graph it. $$x=(y-4)^{2}-1$$