Problem to solve
Solve \[\frac{x}{2}-3z=-2\], \[3y-\frac{z}{2}=2\], \[x+3y-z=5\]
Solution
STEP 1
Solve the following system:
{-3 z + x/2 = -2 | (equation 1)
-z/2 + 3 y = 2 | (equation 2)
x + 3 y - z = 5 | (equation 3)
STEP 2
Swap equation 1 with equation 3:
{x + 3 y - z = 5 | (equation 1)
0 x+3 y - z/2 = 2 | (equation 2)
x/2 + 0 y - 3 z = -2 | (equation 3)
STEP 3
Multiply equation 2 by 2:
{x + 3 y - z = 5 | (equation 1)
0 x+6 y - z = 4 | (equation 2)
x/2 + 0 y - 3 z = -2 | (equation 3)
STEP 4
Multiply equation 3 by 2:
{x + 3 y - z = 5 | (equation 1)
0 x+6 y - z = 4 | (equation 2)
x + 0 y - 6 z = -4 | (equation 3)
STEP 5
Subtract equation 1 from equation 3:
{x + 3 y - z = 5 | (equation 1)
0 x+6 y - z = 4 | (equation 2)
0 x - 3 y - 5 z = -9 | (equation 3)
STEP 6
Multiply equation 3 by -1:
{x + 3 y - z = 5 | (equation 1)
0 x+6 y - z = 4 | (equation 2)
0 x+3 y + 5 z = 9 | (equation 3)
STEP 7
Subtract 1/2 × (equation 2) from equation 3:
{x + 3 y - z = 5 | (equation 1)
0 x+6 y - z = 4 | (equation 2)
0 x+0 y+(11 z)/2 = 7 | (equation 3)
STEP 8
Multiply equation 3 by 2:
{x + 3 y - z = 5 | (equation 1)
0 x+6 y - z = 4 | (equation 2)
0 x+0 y+11 z = 14 | (equation 3)
STEP 9
Divide equation 3 by 11:
{x + 3 y - z = 5 | (equation 1)
0 x+6 y - z = 4 | (equation 2)
0 x+0 y+z = 14/11 | (equation 3)
STEP 10
Add equation 3 to equation 2:
{x + 3 y - z = 5 | (equation 1)
0 x+6 y+0 z = 58/11 | (equation 2)
0 x+0 y+z = 14/11 | (equation 3)
STEP 11
Divide equation 2 by 6:
{x + 3 y - z = 5 | (equation 1)
0 x+y+0 z = 29/33 | (equation 2)
0 x+0 y+z = 14/11 | (equation 3)
STEP 12
Subtract 3 × (equation 2) from equation 1:
{x + 0 y - z = 26/11 | (equation 1)
0 x+y+0 z = 29/33 | (equation 2)
0 x+0 y+z = 14/11 | (equation 3)
STEP 13
Add equation 3 to equation 1:
{x+0 y+0 z = 40/11 | (equation 1)
0 x+y+0 z = 29/33 | (equation 2)
0 x+0 y+z = 14/11 | (equation 3)
STEP 14
Collect results:
Answer: | 
 | {x = 40/11
y = 29/33
z = 14/11