11.2E: Systems of Linear Equations with Three Variables (Exercises)
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For the following exercises, solve the system of three equations using substitution or addition.
11.
0.5x−0.5y=10
−0.2y+0.2x=4
0.1x+0.1z=2
12.
5x+3y−z=5
3x−2y+4z=13
4x+3y+5z=22
13.
x+y+z=1
2x+2y+2z=1
3x+3y=2
14.
2x−3y+z=−1
x+y+z=−4
4x+2y−3z=33
15.
3x+2y−z=−10
x−y+2z=7
−x+3y+z=−2
16.
3x+4z=−11
x−2y=5
4y−z=−10
17.
2x−3y+z=0
2x+4y−3z=0
6x−2y−z=0
18.
6x−4y−2z=2
3x+2y−5z=4
6y−7z=5
For the following exercises, write a system of equations to solve each problem. Solve the system of equations.
19. Three odd numbers sum up to 61 . The smaller is one-third the larger and the middle number is 16 less than the larger. What are the three numbers?
20. A local theatre sells out for their show. They sell all 500 tickets for a total purse of $8,070.00. The tickets were priced at $15 for students, $12 for children, and $18 for adults. If the band sold three times as many adult tickets as children's tickets, how many of each type was sold?