See Problem 3.

Solve each system of equations using a matrix equation. Check your answers.

17. { x + 3 y = 5 x + 4 y = 6 left brace . table with 2 rows and 1 column , row1 column 1 , x plus 3 y equals 5 , row2 column 1 , x plus 4 y equals 6 , end table
18. { p − 3 q = − 1 − 5 q + 16 q = 5 left brace . table with 2 rows and 2 columns , row1 column 1 , p minus 3 q equals , column 2 negative 1 , row2 column 1 , negative 5 q plus 16 q equals , column 2 5 , end table
19. { 300 x − y = 130 200 x + y = 120 left brace . table with 2 rows and 1 column , row1 column 1 , 300 x minus y equals 130 , row2 column 1 , 200 x plus y equals 120 , end table
20. { x + 5 y = − 4 x + 6 y = − 5 left brace . table with 2 rows and 1 column , row1 column 1 , x plus 5 y equals negative 4 , row2 column 1 , x plus 6 y equals negative 5 , end table
21. { 2 x + 3 y = 12 x + 2 y = 7 left brace . table with 2 rows and 2 columns , row1 column 1 , 2 x plus 3 y equals , column 2 12 , row2 column 1 , x plus 2 y equals , column 2 7 , end table
22. { 2 x + 3 y = 5 x + 2 y = 6 left brace . table with 2 rows and 2 columns , row1 column 1 , 2 x plus 3 y equals , column 2 5 , row2 column 1 , x plus 2 y equals , column 2 6 , end table
23. { x + y + z = 4 4 x + 5 y = 3 y − 3 z = − 10 left brace . table with 3 rows and 2 columns , row1 column 1 , x plus y plus z equals , column 2 4 , row2 column 1 , 4 x plus 5 y equals , column 2 3 , row3 column 1 , y minus 3 z equals , column 2 negative 10 , end table
24. { 9 y + 2 z = 18 3 x + 2 y + z = 5 x − y = − 1 left brace . table with 3 rows and 2 columns , row1 column 1 , 9 y plus 2 z equals , column 2 18 , row2 column 1 , 3 x plus 2 y plus z equals , column 2 5 , row3 column 1 , x minus y equals , column 2 negative 1 , end table
25. { 9 y + 2 z = 14 3 x + 2 y + z = 5 x − y = − 1 left brace . table with 3 rows and 2 columns , row1 column 1 , 9 y plus 2 z equals , column 2 14 , row2 column 1 , 3 x plus 2 y plus z equals , column 2 5 , row3 column 1 , x minus y equals , column 2 negative 1 , end table

See Problem 4.

26. Fitness Your classmate is starting a new fitness program. He is planning to ride his bicycle 60 minutes every day. He burns 7 Calories per minute bicycling at 11 mph and 11.75 Calories per minute bicycling at 15 mph. How long should he bicycle at each speed to burn 600 calories per hour?

B Apply

27. Think About a Plan Suppose you want to fill nine 1-lb tins with a snack mix. You plan to buy almonds for $2.45/lb, peanuts for $1.85/lb, and raisins for $.80/lb. You want the mix to contain twice as much nuts as raisins by weight. If you spend exactly $15, how much of each ingredient should you buy?
    • How many equations do you need to represent this situation?
    • How can you represent this system using a matrix equation?
28. Nutrition Suppose you are making a trail mix for your friends and want to fill three 1-lb bags. Almonds cost $2.25/lb, peanuts cost $1.30/lb, and raisins cost $.90/lb. You want each bag to contain twice as much nuts as raisins by weight. If you spent $4.45, how much of each ingredient did you buy?

Solve each system.

29. { − 3 x + 4 y = 2 x − y = − 1 left brace . table with 2 rows and 2 columns , row1 column 1 , negative 3 x plus 4 y equals , column 2 2 , row2 column 1 , x minus y equals , column 2 negative 1 , end table
30. { x + 2 y = 10 3 x + 5 y = 26 left brace . table with 2 rows and 2 columns , row1 column 1 , x plus 2 y equals , column 2 10 , row2 column 1 , 3 x plus 5 y equals , column 2 26 , end table
31. { x − 3 y = − 1 − 6 x + 19 y = 6 left brace . table with 2 rows and 2 columns , row1 column 1 , x minus 3 y equals , column 2 negative 1 , row2 column 1 , negative 6 x plus 19 y equals , column 2 6 , end table
32. { x = 5 − y 3 y = z x + z = 7 left brace . table with 3 rows and 2 columns , row1 column 1 , x equals , column 2 5 minus y , row2 column 1 , 3 y equals , column 2 z , row3 column 1 , x plus z equals , column 2 7 , end table
33. { − x = − 4 − z 2 y = z − 1 x = 6 − y − z left brace . table with 3 rows and 2 columns , row1 column 1 , negative x equals , column 2 negative 4 minus z , row2 column 1 , 2 y equals , column 2 z minus 1 , row3 column 1 , x equals , column 2 6 minus y minus z , end table
34. { − b + 2 c = 4 a + b − c = − 10 2 a + 3 c = 1 left brace . table with 3 rows and 2 columns , row1 column 1 , negative b plus 2 c equals , column 2 4 , row2 column 1 , eh plus b minus c equals , column 2 negative 10 , row3 column 1 , 2 eh plus 3 c equals , column 2 1 , end table
35. { x + y + z = 4 4 x + 5 y = 4 y − 3 z = − 9 left brace . table with 3 rows and 2 columns , row1 column 1 , x plus y plus z equals , column 2 4 , row2 column 1 , 4 x plus 5 y equals , column 2 4 , row3 column 1 , y minus 3 z equals , column 2 negative 9 , end table
36. { x + y + z = 4 4 x + 5 y = 3 y − 3 z = − 10 left brace . table with 3 rows and 2 columns , row1 column 1 , x plus y plus z equals , column 2 4 , row2 column 1 , 4 x plus 5 y equals , column 2 3 , row3 column 1 , y minus 3 z equals , column 2 negative 10 , end table
37. { − 2 w + x + y = 0 − w + 2 x − y + z = 1 − 2 w + 3 x + 3 y + 2 z = 6 w + x + 2 y + z = 5 left brace . table with 4 rows and 1 column , row1 column 1 , negative 2 w plus x plus y equals 0 , row2 column 1 , negative w plus 2 x minus y plus z equals 1 , row3 column 1 , negative 2 w plus 3 x plus 3 y plus 2 z equals 6 , row4 column 1 , w plus x plus 2 y plus z equals 5 , end table
38. { − 2 w + x + y = − w + 2 x − y + z = − 2 w + 3 x + 3 y + 2 z = w + x + 2 y + z = − 2 − 4 2 6 left brace . table with 4 rows and 1 column , row1 column 1 , negative 2 w plus x plus y equals , row2 column 1 , negative w plus 2 x minus y plus z equals , row3 column 1 , negative 2 w plus 3 x plus 3 y plus 2 z equals , row4 column 1 , w plus x plus 2 y plus z equals , end table . table with 4 rows and 1 column , row1 column 1 , negative 2 , row2 column 1 , negative 4 , row3 column 1 , 2 , row4 column 1 , 6 , end table

Solve each matrix equation. If the coefficient matrix has no inverse, write no unique solution.

39. [ 1 1 1 2 ] [ x y ] = [ 8 10 ] . matrix with 2 rows and 2 columns , row1 column 1 , 1 , column 2 1 , row2 column 1 , 1 , column 2 2 , end matrix , matrix with 2 rows and 1 column , row1 column 1 , x , row2 column 1 , y , end matrix . equals . matrix with 2 rows and 1 column , row1 column 1 , 8 , row2 column 1 , 10 , end matrix
40. [ 2 − 3 − 4 6 ] [ a b ] = [ 1 − 2 ] . matrix with 2 rows and 2 columns , row1 column 1 , 2 , column 2 negative 3 , row2 column 1 , negative 4 , column 2 6 , end matrix , matrix with 2 rows and 1 column , row1 column 1 , eh , row2 column 1 , b , end matrix . equals . matrix with 2 rows and 1 column , row1 column 1 , 1 , row2 column 1 , negative 2 , end matrix
41. [ 2 1 4 3 ] [ x y ] = [ 10 − 2 ] . matrix with 2 rows and 2 columns , row1 column 1 , 2 , column 2 1 , row2 column 1 , 4 , column 2 3 , end matrix , matrix with 2 rows and 1 column , row1 column 1 , x , row2 column 1 , y , end matrix . equals . matrix with 2 rows and 1 column , row1 column 1 , 10 , row2 column 1 , negative 2 , end matrix

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