C Challenge

Open-Ended Complete each system for the given number of solutions.

42. infinitely many

    { x + y = 7 2 x + 2 y = □ left brace . table with 2 rows and 3 columns , row1 column 1 , x plus , column 2 y equals , column 3 7 , row2 column 1 , 2 x plus , column 2 2 y equals , column 3 white square , end table

43. one solution

    { x + y + z = 7 y + z = □ z = □ left brace . table with 3 rows and 1 column , row1 column 1 , x plus y plus z equals 7 , row2 column 1 , y plus z equals white square , row3 column 1 , z equals white square , end table

44. no solution

    { x + y + z = 7 y + z = □ y + z = □ left brace . table with 3 rows and 1 column , row1 column 1 , x plus y plus z equals 7 , row2 column 1 , y plus z equals white square , row3 column 1 , y plus z equals white square , end table

Solve the system of equations using a matrix. (Hint: Start by substituting m = 1 x bold italic m equals , 1 over bold italic x  and n = 1 y . bold italic n equals , 1 over bold italic y , . )

45. { 4 x + 1 y = 1 8 x + 4 y = 3 left brace . table with 2 rows and 1 column , row1 column 1 , 4 over x , plus , 1 over y , equals 1 , row2 column 1 , 8 over x , plus , 4 over y , equals 3 , end table
46. { 4 x − 2 y = 1 10 x + 20 y = 0 left brace . table with 2 rows and 1 column , row1 column 1 , 4 over x , minus , 2 over y , equals 1 , row2 column 1 , 10 over x , plus , 20 over y , equals 0 , end table
47. { 7 x + 3 y = 5 2 x + 1 y = − 1 left brace . table with 2 rows and 1 column , row1 column 1 , 7 over x , plus , 3 over y , equals 5 , row2 column 1 , 2 over x , plus , 1 over y , equals negative 1 , end table

Standardized Test Prep

SAT/ACT

48. Which equation represents a line with a slope of 1 2 1 half  and a y-intercept of 3 4 ? 3 fourths , question mark
    1. y = 1 2 x − 3 4 y equals , 1 half , x minus , 3 fourths
    2. y = 3 4 x − 1 2 y equals , 3 fourths , x minus , 1 half
    3. y = 1 2 x + 3 4 y equals , 1 half , x plus , 3 fourths
    4. y = 3 4 x + 1 2 y equals , 3 fourths , x plus , 1 half
49. Which graph best represents the solution of the inequality y ≤ 2 | x − 1 | − 4 ? y less than or equal to 2 vertical line x minus 1 vertical line negative 4 question mark
    6. 
    7. 
    8. 
    9. 

Short Response

50. At what point do the graphs of the equations y = 7 x − 3 y equals 7 , x minus , 3  and − 6 x + y = 2 negative 6 x plus y equals 2  intersect?

Mixed Review

See Lesson 1-5.

Solve each inequality. Graph the solution.

51. 12 ≥ 2 ( 4 x + 1 ) + 22 12 greater than or equal to 2 open 4 x plus 1 close plus 22
52. 2 x − ( 3 x + 5 ) ≤ 30 2 x minus open 3 x plus 5 close less than or equal to 30
53. 4 x + 5 − 3 x ≤ 2 x + 1 4 x plus 5 minus 3 x less than or equal to 2 x plus 1

See Lesson 1-6.

Solve each equation. Check your answers.

54. | 2 y − 3 | = 12 vertical line 2 y minus 3 vertical line equals 12
55. | 4 x | = 40 vertical line 4 x vertical line equals 40
56. | 2 y − 4 | = 16 vertical line 2 y minus 4 vertical line equals 16

Get Ready! To prepare for Lesson 4-1, do Exercises 57 and 58.

See Lesson 2-6.

Write an equation for each transformation of y = x.

57. vertical stretch by a factor of 2.
58. vertical compression by a factor of 1 3 1 third

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