See Problems 3 and 4.

Solve each system by substitution. Check your answers.

21. { x + 2 y + 3 z = 6   y + 2 z = 0     z = 2 left brace . table with 3 rows and 4 columns , row1 column 1 , x plus , column 2 2 y plus , column 3 3 z equals , column 4 6 , row2 column 1 , , column 2 y plus , column 3 2 z equals , column 4 0 , row3 column 1 , , column 2 , column 3 z equals , column 4 2 , end table
22. { 3 a + b + c = 7 a + 3 b − c = 13 b = 2 a − 1   left brace . table with 3 rows and 4 columns , row1 column 1 , 3 eh plus , column 2 b plus , column 3 c equals , column 4 7 , row2 column 1 , eh plus , column 2 3 b minus , column 3 c equals , column 4 13 , row3 column 1 , b equals , column 2 2 eh minus , column 3 1 , column 4 , end table
23. { 5 r − 4 s − 3 t = 3 t = s + r r = 3 s + 1 left brace . table with 3 rows and 1 column , row1 column 1 , 5 r minus 4 s minus 3 t equals 3 , row2 column 1 , t equals s plus r , row3 column 1 , r equals 3 s plus 1 , end table
24. { 13 = 3 x − y   4 y − 3 x + 2 z = − 3 z = 2 x − 4 y   left brace . table with 3 rows and 4 columns , row1 column 1 , 13 equals , column 2 3 x minus , column 3 y , column 4 , row2 column 1 , 4 y minus , column 2 3 x plus , column 3 2 z equals , column 4 negative 3 , row3 column 1 , z equals , column 2 2 x minus , column 3 4 y , column 4 , end table
25. { x + 3 y − z = − 4 2 x − y + 2 z = 13 3 x − 2 y − z = − 9 left brace . table with 3 rows and 4 columns , row1 column 1 , x plus , column 2 3 y minus , column 3 z equals , column 4 negative 4 , row2 column 1 , 2 x minus , column 2 y plus , column 3 2 z equals , column 4 13 , row3 column 1 , 3 x minus , column 2 2 y minus , column 3 z equals , column 4 negative 9 , end table
26. { x − 4 y + z = 6 2 x + 5 y − z = 7 2 x − y − z = 1 left brace . table with 3 rows and 4 columns , row1 column 1 , x minus , column 2 4 y plus , column 3 z equals , column 4 6 , row2 column 1 , 2 x plus , column 2 5 y minus , column 3 z equals , column 4 7 , row3 column 1 , 2 x minus , column 2 y minus , column 3 z equals , column 4 1 , end table
27. { x − y + 2 z = 7 2 x + y + z = 8 x − z = 5 left brace . table with 3 rows and 4 columns , row1 column 1 , x minus , column 2 y plus , column 3 2 z equals , column 4 7 , row2 column 1 , 2 x plus , column 2 y plus , column 3 z equals , column 4 8 , row3 column 1 , x , column 2 minus , column 3 z equals , column 4 5 , end table
28. { x + y + z = 2 x + 2 z = 5 2 x + y − z = − 1 left brace . table with 3 rows and 4 columns , row1 column 1 , x plus , column 2 y plus , column 3 z equals , column 4 2 , row2 column 1 , x , column 2 plus , column 3 2 z equals , column 4 5 , row3 column 1 , 2 x plus , column 2 y minus , column 3 z equals , column 4 negative 1 , end table
29. { 5 x − y + z = 4 x + 2 y − z = 5 2 x + 3 y − 3 z = 5 left brace . table with 3 rows and 4 columns , row1 column 1 , 5 x minus , column 2 y plus , column 3 z equals , column 4 4 , row2 column 1 , x plus , column 2 2 y minus , column 3 z equals , column 4 5 , row3 column 1 , 2 x plus , column 2 3 y minus , column 3 3 z equals , column 4 5 , end table
30. Manufacturing In a factory there are three machines, A, B, and C. When all three machines are working, they produce 287 bolts per hour. When only machines A and C are working, they produce 197 bolts per hour. When only machines A and B are working, they produce 202 bolts per hour. How many bolts can each machine produce per hour?

B Apply

31. Think About a Plan In triangle PQR, the measure of angle Q is three times the measure of angle P. The measure of angle R is 20°more than the measure of angle P. Find the measure of each angle.
    • What are the unknowns in this problem?
    • What system of equations represents this situation?
    • Which method of solving looks easier for this problem?
32. Sports A stadium has 49,000 seats. Seats sell for $25 in Section A, $20 in Section B, and $15 in Section C. The number of seats in Section A equals the total number of seats in Sections B and C. Suppose the stadium takes in $1,052,000 from each sold-out event. How many seats does each section hold?

Solve each system using any method.

33. { x − 3 y + 2 z = 11 − x + 4 y + 3 z = 5 2 x − 2 y − 4 z = 2 left brace . table with 3 rows and 4 columns , row1 column 1 , x minus , column 2 3 y plus , column 3 2 z equals , column 4 11 , row2 column 1 , negative x plus , column 2 4 y plus , column 3 3 z equals , column 4 5 , row3 column 1 , 2 x minus , column 2 2 y minus , column 3 4 z equals , column 4 2 , end table
34. { x + 2 y + z = 4 2 x − y + 4 z = − 8 − 3 x + y − z = − 1 left brace . table with 3 rows and 4 columns , row1 column 1 , x plus , column 2 2 y plus , column 3 z equals , column 4 4 , row2 column 1 , 2 x minus , column 2 y plus , column 3 4 z equals , column 4 negative 8 , row3 column 1 , negative 3 x plus , column 2 y minus , column 3 z equals , column 4 negative 1 , end table
35. { 4 x − y + 2 z = − 6 − 2 x + 3 y − z = 8   2 y + 3 z = − 5 left brace . table with 3 rows and 4 columns , row1 column 1 , 4 x minus , column 2 y plus , column 3 2 z equals , column 4 negative 6 , row2 column 1 , negative 2 x plus , column 2 3 y minus , column 3 z equals , column 4 8 , row3 column 1 , , column 2 2 y plus , column 3 3 z equals , column 4 negative 5 , end table
36. { 4 a + 2 b + c = 2 5 a − 3 b + 2 c = 17 a − 5 b = 3 left brace . table with 3 rows and 1 column , row1 column 1 , 4 eh plus 2 b plus c equals 2 , row2 column 1 , 5 eh minus 3 b plus 2 c equals 17 , row3 column 1 , eh minus 5 b equals 3 , end table
37. { 4 x − 2 y + 5 z = 6 3 x + 3 y + 8 z = 4 x − 5 y − 3 z = 5 left brace . table with 3 rows and 4 columns , row1 column 1 , 4 x minus , column 2 2 y plus , column 3 5 z equals , column 4 6 , row2 column 1 , 3 x plus , column 2 3 y plus , column 3 8 z equals , column 4 4 , row3 column 1 , x minus , column 2 5 y minus , column 3 3 z equals , column 4 5 , end table
38. { 2 l + 2 w + h = 72 l = 3 w h = 2 w left brace . table with 3 rows and 1 column , row1 column 1 , 2 l plus 2 w plus h equals 72 , row2 column 1 , l equals 3 w , row3 column 1 , h equals 2 w , end table
39. { 6 x + y − 4 z = − 8   y 4 − z 6 = 0 2 x − z = − 2 left brace . table with 3 rows and 4 columns , row1 column 1 , 6 x plus , column 2 y minus , column 3 4 z equals , column 4 negative 8 , row2 column 1 , , column 2 y over 4 , minus , column 3 z over 6 , equals , column 4 0 , row3 column 1 , 2 x , column 2 minus , column 3 z equals , column 4 negative 2 , end table
40. { 4 y + 2 x = 6 − 3 z x + z − 2 y = − 5 x − 2 z = 3 y − 7 left brace . table with 3 rows and 4 columns , row1 column 1 , 4 y plus , column 2 2 x equals , column 3 6 minus , column 4 3 z , row2 column 1 , x plus , column 2 z minus , column 3 2 y equals , column 4 negative 5 , row3 column 1 , x minus , column 2 2 z equals , column 3 3 y minus , column 4 7 , end table
41. { 4 x − y + z = − 5 − x + y − z = 5 2 x − z − 1 = y left brace . table with 3 rows and 4 columns , row1 column 1 , 4 x minus , column 2 y plus , column 3 z equals , column 4 negative 5 , row2 column 1 , negative x plus , column 2 y minus , column 3 z equals , column 4 5 , row3 column 1 , 2 x minus , column 2 z minus , column 3 1 equals , column 4 y , end table
42. Finance A worker received a $10,000 bonus and decided to split it among three different accounts. He placed part in a savings account paying 4.5% per year, twice as much in government bonds paying 5%, and the rest in a mutual fund that returned 4%. His income from these investments after one year was $455. How much did the worker place in each account?

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