Systems of Equations and Inequalities

In Problems 5–24, graph each equation of the system. Then solve the system to find the points of intersection.

$$\begin{gathered} y=\sqrt{4-x^2}; \\ y=2x+4 \end{gathered}$$

The graph of the corresponding equation of a linear inequality is a line that separates the xy-plane into two regions. The two regions are called ___ .

In Problems 5–24, graph each equation of the system. Then solve the system to find the points of intersection.

$$\begin{gathered} y=\sqrt{x}; \\ y=2-x \end{gathered}$$

True or False:

The graph of a system of inequalities must have an overlapping region.

In Problems 5–24, graph each equation of the system. Then solve the system to find the points of intersection.

$$\begin{gathered} y=\sqrt{x}; \\ y=6-x \end{gathered}$$

If a graph of a system of linear inequalities cannot be contained in any circle, then it is said to be ___ .

In Problems 5–24, graph each equation of the system. Then solve the system to find the points of intersection.

$$\begin{gathered} x=2y; \\ x=y^2-2y \end{gathered}$$

In Problems 5–24, graph each equation of the system. Then solve the system to find the points of intersection.

$$\begin{gathered} y=x-1; \\ y=x^2-6x+9 \end{gathered}$$

In Problems 5–24, graph each equation of the system. Then solve the system to find the points of intersection.

$$\begin{gathered} x^2+y^2=4; \\ {x}^2+2x+y^2=0 \end{gathered}$$

In Problems 5–24, graph each equation of the system. Then solve the system to find the points of intersection.

$$\begin{gathered} x^2+y^2=8; \\ {x}^2+y^2+4y=0 \end{gathered}$$

In Problems 5–24, graph each equation of the system. Then solve the system to find the points of intersection.

$$\begin{gathered} y=3x-5; \\ {x}^2+y^2=5 \end{gathered}$$

In Problems 5–24, graph each equation of the system. Then solve the system to find the points of intersection.

$$\begin{gathered} x^2+y^2=10; \\ y=x+2 \end{gathered}$$

In Problems 5–24, graph each equation of the system. Then solve the system to find the points of intersection.

$$\begin{gathered} x^2+y^2=4; \\ y^2-x=4 \end{gathered}$$

In Problems 5–24, graph each equation of the system. Then solve the system to find the points of intersection.

$$\begin{gathered} x^2+y^2=16; \\ {x}^2-2y=8 \end{gathered}$$

In Problems 5–24, graph each equation of the system. Then solve the system to find the points of intersection.

$$\begin{gathered} xy=4; \\ {x}^2+y^2=8 \end{gathered}$$

In Problems 5–24, graph each equation of the system. Then solve the system to find the points of intersection.

$$\begin{gathered} x^2=y; \\ xy=1 \end{gathered}$$

In Problems 5–24, graph each equation of the system. Then solve the system to find the points of intersection.

$$\begin{gathered} x^2+y^2=4; \\ y=x^2-9 \end{gathered}$$

In Problems 5–24, graph each equation of the system. Then solve the system to find the points of intersection.

$$\begin{gathered} xy=1; \\ y=2x+1 \end{gathered}$$

graph each equation of the system. Then solve the system to find the points of intersection.

$\left\{\begin{array}{l}y = x^2 - 4 \\ y = 6x - 13\end{array}\right.$

graph each equation of the system. Then solve the system to find the points of intersection.

$\left\{\begin{array}{l}y{ }^2+x^2=10 \\ xy=3\end{array}\right.$

Find the center and radius of the circle $x^2+y^2-2x+4y-11=0$. Graph the circle.

Graph the inequality by hand.

$x\ge 0$

Graph the inequality by hand.

$y\ge 0$

Graph the inequality by hand.

$x\ge 4$

graph each equation of the system. Then solve the system to find the points of intersection.

$\left\{\begin{array}{l}2x^2+ y^2 =18 \\ xy=4\end{array}\right.$

graph each equation of the system. Then solve the system to find the points of intersection.

$\left\{\begin{array}{l} x^2 -y^2=21\\ x+y=7\end{array}\right.$

Graph each equation of the system. Then solve the system to find the points of intersection.

$\left\{\begin{array}{l}y=2x+1\\ 2x^2+y^2=1\end{array}\right.$

Graph each equation of the system. Then solve the system to find the points of intersection.

$\left\{\begin{array}{l}{x}^2-4y^2=16\\ 2y-x=2\end{array}\right.$

Graph each equation of the system. Then solve the system to find the points of intersection.

$\left\{\begin{array}{l}x+y+1=0\\ x^2+y^2+6y-x=-5\end{array}\right.$

Graph each equation of the system. Then solve the system to find the points of intersection.

$\left\{\begin{array}{l}2x^2-xy+y^2=8\\ xy=4\end{array}\right.$

Graph each equation of the system. Then solve the system to find the points of intersection.

$\left\{\begin{array}{l}4x^2-3xy+9y^2=15\\ 2x+3y=5\end{array}\right.$

Graph each equation of the system. Then solve the system to find the points of intersection.

$\left\{\begin{array}{l}2y^2-3xy+6y+2x+4=0\\ 2x-3y+4=0\end{array}\right.$

graph each equation of the system. Then solve the system to find the points of intersection.

$\left\{\begin{array}{l}{x}^2-4y^2+7=0\\ 3x^2+y^2=31\end{array}\right.$

Graph each equation of the system. Then solve the system to find the points of intersection.

$$\begin{gathered} 3x^2-2y^2+5=0 \\ 2x^2-y^2+2=0 \end{gathered}$$

graph each equation of the system. Then solve the system to find the points of intersection.

$\left\{\begin{array}{l}7x^2-3y^2+5=0\\ 3x^2+5y^2=12\end{array}\right.$

graph each equation of the system. Then solve the system to find the points of intersection.

$$\begin{gathered} x^2-3y^2+1=0 \\ 2x^2-7y^2+5=0 \end{gathered}$$

graph each equation of the system. Then solve the system to find the points of intersection.

$$\begin{gathered} x^2+2xy=10 \\ 3x^2-xy=2 \end{gathered}$$

graph each equation of the system. Then solve the system to find the points of intersection.

$$\begin{gathered} 5xy+13y^2+36=0 \\ xy+7y^2=6 \end{gathered}$$

graph each equation of the system. Then solve the system to find the points of intersection.

$$\begin{gathered} 2x^2+y^2=2 \\ {x}^2-2y^2+8=0 \end{gathered}$$

graph each equation of the system. Then solve the system to find the points of intersection.

$$\begin{gathered} y^2-x^2+4=0 \\ 2x^2+3y^2=6 \end{gathered}$$

graph each equation of the system. Then solve the system to find the points of intersection.

$$\begin{gathered} x^2+2y^2=16 \\ 4x^2-y^2=24 \end{gathered}$$

graph each equation of the system. Then solve the system to find the points of intersection.

$$\begin{gathered} 4x^2+3y^2=4 \\ 2x^2-6y^2=-3 \end{gathered}$$

Solve the system. Use any method you wish.

$\left\{\begin{array}{l}\frac{5}{x^2}-\frac{2}{y^2}+3=0\\ \frac{3}{x^2}+\frac{1}{y^2}=7\end{array}\right.$

Solve the system. Use any method you wish.

$\left\{\begin{array}{l}\frac{2}{x^2}-\frac{3}{y^2}+1=0\\ \frac{6}{x^2}-\frac{7}{y^2}+2=0\end{array}\right.$

Solve the system. Use any method you wish.

$\left\{\begin{array}{l}\frac{1}{x^4}+\frac{6}{y^4}=6\\ \frac{2}{x^4}-\frac{2}{y^4}=19\end{array}\right.$

Solve the system. Use any method you wish.

$\left\{\begin{array}{l}\frac{1}{x^4}-\frac{1}{y^4}=1\\ \frac{1}{x^4}+\frac{1}{y^4}=4\end{array}\right.$

Solve the system. Use any method you wish.

$\left\{\begin{array}{l}{x}^2-3xy+2y^2=0\\ x^2+xy=6\end{array}\right.$

Solve the system. Use any method you wish.

$\left\{\begin{array}{l}{x}^2-xy-2y^2=0\\ xy+x+6=0\end{array}\right.$

In Problems $25-54$, solve each system. Use any method you wish.

$\left\{\begin{array}{l}\ln x=4 \ln y\\ {\log }_{3}x=2+2{\log }_{3}y\end{array}\right.$

In Problems $25-54$, solve each system. Use any method you wish.

$\left\{\begin{array}{l}\ln x=5 \ln y\\ {\log }_{2}x=3+2{\log }_{2}y\end{array}\right.$