6.3E: 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?