C Challenge

43. Open-Ended Write your own system with three variables. Begin by choosing the solution. Then write three equations that are true for your solution. Use elimination to solve the system.
44. Geometry Refer to the regular five-pointed star below. Write and solve a system of three equations to find the measure of each labeled angle.

    
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45. 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.

Standardized Test Prep

GRIDDED RESPONSE

SAT/ACT

46. What is the value of z in the solution of the system? { y = − 2 x + 10 − x + y − 2 z = − 2 3 x − 2 y + 4 z = 7 left brace . table with 3 rows and 1 column , row1 column 1 , y equals negative 2 x plus 10 , row2 column 1 , negative x plus y minus 2 z equals negative 2 , row3 column 1 , 3 x minus 2 y plus 4 z equals 7 , end table
47. What is the x-intercept of the line below after it is translated up 3 units?

    

48. Suppose y varies directly with x, and y = 15 when x = 10. What is y when x = 22?

49. A theater has 490 seats. Seats sell for $25 on the floor, $20 in the mezzanine, and $15 in the balcony. The number of seats on the floor equals the total number of seats in the mezzanine and balcony. Suppose the theater takes in $10,520 from each sold-out event. How many seats does the mezzanine section hold?

Mixed Review

See Lesson 3-4.

50. Maximize the objective function P = x + 3y under the given constraints. At what vertex does this maximum value occur?

    { x + y ≤ 5 x + 2 y ≤ 8 x ≥ 0 , y ≥ 0 left brace . table with 3 rows and 4 columns , row1 column 1 , x plus , column 2 y , column 3 less than or equal to , column 4 5 , row2 column 1 , x plus , column 2 2 y , column 3 less than or equal to , column 4 8 , row3 column 1 , x greater than or equal to , column 2 0 comma y , column 3 greater than or equal to , column 4 0 , end table

See Lesson 1-5.

Solve each inequality. Graph the solution on a number line.

51. − 4 x + 3 ≤ 9 negative 4 x plus 3 less than or equal to 9
52. − ( x + 4 ) − 3 ≥ 11 negative open x plus 4 close minus 3 greater than or equal to 11
53. 2 ( 3 x − 1 ) < x − 7 2 open 3 x minus 1 close less than x minus 7

Get Ready! To prepare for Lesson 3-6, do Exercises 54–56.

See Lesson 3-2.

Solve each system using elimination.

54. { x + 4 y = 12 2 x − 8 y = 4 left brace . table with 2 rows and 3 columns , row1 column 1 , x plus , column 2 4 y equals , column 3 12 , row2 column 1 , 2 x minus , column 2 8 y equals , column 3 4 , end table
55. { 4 x + 8 y = − 6 6 x + 12 y = − 9 left brace . table with 2 rows and 3 columns , row1 column 1 , 4 x plus , column 2 8 y equals , column 3 negative 6 , row2 column 1 , 6 x plus , column 2 12 y equals , column 3 negative 9 , end table
56. { 4 y − 2 x = 6 8 y = 4 x − 12 left brace . table with 2 rows and 3 columns , row1 column 1 , 4 y minus , column 2 2 x equals , column 3 6 , row2 column 1 , 8 y equals , column 2 4 x minus , column 3 12 , end table

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