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Mathematics LibreTexts

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.

0.5x0.5y=10

0.2y+0.2x=4
0.1x+0.1z=2

12.

5x+3yz=5

3x2y+4z=13
4x+3y+5z=22

13.

x+y+z=1

2x+2y+2z=1
3x+3y=2

14.

2x3y+z=1

x+y+z=4
4x+2y3z=33

15.

3x+2yz=10

xy+2z=7
x+3y+z=2

16.

3x+4z=11

x2y=5
4yz=10

17.

2x3y+z=0

2x+4y3z=0
6x2yz=0

18.

6x4y2z=2

3x+2y5z=4
6y7z=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?


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