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.

$0.5 x-0.5 y=10$

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

12.

$5 x+3 y-z=5$

$3 x-2 y+4 z=13$
$4 x+3 y+5 z=22$

13.

$x+y+z=1$

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

14.

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

$x+y+z=-4$
$4 x+2 y-3 z=33$

15.

$3 x+2 y-z=-10$

$x-y+2 z=7$
$-x+3 y+z=-2$

16.

$3 x+4 z=-11$

$ x-2 y=5$
$4 y-z=-10$

17.

$2 x-3 y+z=0$

$2 x+4 y-3 z=0 $
$6 x-2 y-z=0 $

18.

$6 x-4 y-2 z=2 $

$3 x+2 y-5 z=4 $
$6 y-7 z=5$

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?