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Solve the following system:
{x+2 y = 20 |     (equation 1)
y+2 z = 9 |     (equation 2)
2 x+z = 22 |     (equation 3)
Swap equation 1 with equation 3:
{2 x+0 y+z = 22 |     (equation 1)
0 x+y+2 z = 9 |     (equation 2)
x+2 y+0 z = 20 |     (equation 3)
Subtract 1/2 × (equation 1) from equation 3:
{2 x+0 y+z = 22 |     (equation 1)
0 x+y+2 z = 9 |     (equation 2)
0 x+2 y-z/2 = 9 |     (equation 3)
Multiply equation 3 by 2:
{2 x+0 y+z = 22 |     (equation 1)
0 x+y+2 z = 9 |     (equation 2)
0 x+4 y-z = 18 |     (equation 3)
Swap equation 2 with equation 3:
{2 x+0 y+z = 22 |     (equation 1)
0 x+4 y-z = 18 |     (equation 2)
0 x+y+2 z = 9 |     (equation 3)
Subtract 1/4 × (equation 2) from equation 3:
{2 x+0 y+z = 22 |     (equation 1)
0 x+4 y-z = 18 |     (equation 2)
0 x+0 y+(9 z)/4 = 9/2 |     (equation 3)
Multiply equation 3 by 4/9:
{2 x+0 y+z = 22 |     (equation 1)
0 x+4 y-z = 18 |     (equation 2)
0 x+0 y+z = 2 |     (equation 3)
Add equation 3 to equation 2:
{2 x+0 y+z = 22 |     (equation 1)
0 x+4 y+0 z = 20 |     (equation 2)
0 x+0 y+z = 2 |     (equation 3)
Divide equation 2 by 4:
{2 x+0 y+z = 22 |     (equation 1)
0 x+y+0 z = 5 |     (equation 2)
0 x+0 y+z = 2 |     (equation 3)
Subtract equation 3 from equation 1:
{2 x+0 y+0 z = 20 |     (equation 1)
0 x+y+0 z = 5 |     (equation 2)
0 x+0 y+z = 2 |     (equation 3)
Divide equation 1 by 2:
{x+0 y+0 z = 10 |     (equation 1)
0 x+y+0 z = 5 |     (equation 2)
0 x+0 y+z = 2 |     (equation 3)
Collect results:
Answer: | 
| {x = 10
y = 5
z = 2

Nov 6, 2015
 #2
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Nov 6, 2015
 #1
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Nov 6, 2015

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