Problem to solve
Solve \[-\frac{3x}{2}+3y+z=2\], \[3x-y+z=5\], \[\frac{x}{3}-y+z=2\]
Solution
STEP 1
Solve the following system:
{-(3 x)/2 + 3 y + z = 2 | (equation 1)
3 x - y + z = 5 | (equation 2)
x/3 - y + z = 2 | (equation 3)
STEP 2
Swap equation 1 with equation 2:
{3 x - y + z = 5 | (equation 1)
-(3 x)/2 + 3 y + z = 2 | (equation 2)
x/3 - y + z = 2 | (equation 3)
STEP 3
Add 1/2 × (equation 1) to equation 2:
{3 x - y + z = 5 | (equation 1)
0 x+(5 y)/2 + (3 z)/2 = 9/2 | (equation 2)
x/3 - y + z = 2 | (equation 3)
STEP 4
Multiply equation 2 by 2:
{3 x - y + z = 5 | (equation 1)
0 x+5 y + 3 z = 9 | (equation 2)
x/3 - y + z = 2 | (equation 3)
STEP 5
Multiply equation 3 by 3:
{3 x - y + z = 5 | (equation 1)
0 x+5 y + 3 z = 9 | (equation 2)
x - 3 y + 3 z = 6 | (equation 3)
STEP 6
Subtract 1/3 × (equation 1) from equation 3:
{3 x - y + z = 5 | (equation 1)
0 x+5 y + 3 z = 9 | (equation 2)
0 x - (8 y)/3 + (8 z)/3 = 13/3 | (equation 3)
STEP 7
Multiply equation 3 by 3:
{3 x - y + z = 5 | (equation 1)
0 x+5 y + 3 z = 9 | (equation 2)
0 x - 8 y + 8 z = 13 | (equation 3)
STEP 8
Swap equation 2 with equation 3:
{3 x - y + z = 5 | (equation 1)
0 x - 8 y + 8 z = 13 | (equation 2)
0 x+5 y + 3 z = 9 | (equation 3)
STEP 9
Add 5/8 × (equation 2) to equation 3:
{3 x - y + z = 5 | (equation 1)
0 x - 8 y + 8 z = 13 | (equation 2)
0 x+0 y+8 z = 137/8 | (equation 3)
STEP 10
Multiply equation 3 by 8:
{3 x - y + z = 5 | (equation 1)
0 x - 8 y + 8 z = 13 | (equation 2)
0 x+0 y+64 z = 137 | (equation 3)
STEP 11
Divide equation 3 by 64:
{3 x - y + z = 5 | (equation 1)
0 x - 8 y + 8 z = 13 | (equation 2)
0 x+0 y+z = 137/64 | (equation 3)
STEP 12
Subtract 8 × (equation 3) from equation 2:
{3 x - y + z = 5 | (equation 1)
0 x - 8 y+0 z = -33/8 | (equation 2)
0 x+0 y+z = 137/64 | (equation 3)
STEP 13
Divide equation 2 by -8:
{3 x - y + z = 5 | (equation 1)
0 x+y+0 z = 33/64 | (equation 2)
0 x+0 y+z = 137/64 | (equation 3)
STEP 14
Add equation 2 to equation 1:
{3 x + 0 y+z = 353/64 | (equation 1)
0 x+y+0 z = 33/64 | (equation 2)
0 x+0 y+z = 137/64 | (equation 3)
STEP 15
Subtract equation 3 from equation 1:
{3 x+0 y+0 z = 27/8 | (equation 1)
0 x+y+0 z = 33/64 | (equation 2)
0 x+0 y+z = 137/64 | (equation 3)
STEP 16
Divide equation 1 by 3:
{x+0 y+0 z = 9/8 | (equation 1)
0 x+y+0 z = 33/64 | (equation 2)
0 x+0 y+z = 137/64 | (equation 3)
STEP 17
Collect results:
Answer: | 
 | {x = 9/8
y = 33/64
z = 137/64