SOLUTION: Can someone please show me how to do the following problem: Solve for X, Y, and Z in the following: 22x + 5y + 7z = 12, 10x + 3y + 2z = 5, 9x + 2y + 12z = 14

Question 2108: Can someone please show me how to do the following problem:
Solve for X, Y, and Z in the following:
22x + 5y + 7z = 12, 10x + 3y + 2z = 5, 9x + 2y + 12z = 14
Answer by DeepaEvangeline(15) (Show Source): You can put this solution on YOUR website!
22x+5y+7z=12 --- (1)
10x+3y+2z=5 --- (2)
9x+2y+12z=14 --- (3)
Eqn(1) x 3
66x+15y+21z=36 --- (4)
eqn(2) x 5
50x+15y+10z=25 --- (5)
Eqn(4) - eqn(5)
16x+11z=11 --- (6)
Eqn(2) x 2
20x+6y+4z=10 --- (7)
eqn(3) x 3
27x+6y+36z=42 --- (8)
Eqn(8) - eqn(7)
7x+32z=32 --- (9)
Eqn(6) x 7 gives
112x+77Z=77 --- (10)
Eqn(9) x 16
112x+512z=512 --- (11)
eqn(11) - eqn(10)
435z=435 => z = 1
Substituting the value of z = 1 in eqn(9) gives
7x+32=32 => x = 0
10x+3y+2z=5 --- (2)
Substituting the value of x = 0 and z = 1 in eqn(2) gives
10.0+3y+2.1=5 => 3y = 3 => y = 1

x=0, y=1, z=1
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