91Ó°ÊÓ

Solve each system of inequalities by graphing. $$ \left\\{\begin{array}{l}{y>x-2} \\ {y \geq|x+2|}\end{array}\right. $$

Solve each system of inequalities by graphing. $$ \left\\{\begin{array}{l}{y>-2} \\ {y \leq-|x-3|}\end{array}\right. $$

Solve each system of inequalities by graphing. \(\left\\{\begin{array}{c}{2 y+x<4} \\ {y-2 x \geq 4}\end{array}\right.\)

Sketch the graph of each equation and find the equation of each trace. $$ 6 x+6 y-12 z=36 $$

Solve each system. $$ \left\\{\begin{aligned} 3 x+2 y+2 z &=-2 \\ 2 x+y-z &=-2 \\ x-3 y+z &=0 \end{aligned}\right. $$

Banking To pay your monthly bills, you can either open a checking account or use an online banking service. A local bank charges \(\$ 3\) per month and \(\$ .40\) per check, while an online services charges a flat fee of \(\$ 9\) per month. a. Write and graph a system of linear equations to model the cost \(c\) of each service for \(b\) bills that you need to pay monthly. b. Find the point of intersection of the two linear models. What does this answer represent? c. If you pay about 12 bills per month, which service should you choose? Explain.

History Exercises 39 and 40 appeared in the book Algebrical Problems, published in \(1824 .\) Write and solve a system for each problem. Ten apples cost a penny, and 25 pears cost two pennies. Suppose I buy 100 apples and pears for 9\(\frac{1}{2}\) pennies. How many of each shall I have?

History Exercises 39 and 40 appeared in the book Algebrical Problems, published in \(1824 .\) Write and solve a system for each problem. A fish was caught whose tail weighed 9 lb. Its head weighed as much as its tail plus half its body. Its body weighed as much as its head and tail. What did the fish weigh?

Open-Ended Write your own system having three variables. Begin by choosing the solution. Then write three equations that are true for your solution. Use elimination to solve the system.

Geometry In the regular polyhedron described below, all faces are congruent polygons. Use a system of three linear equations to find the numbers of vertices, edges, and faces. Every face has five edges and every edge is shared by two faces. Every face has five vertices and every vertex is shared by three faces. The sum of the number of vertices and faces is two more than the number of edges.