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
3 x - y + z = 5
x/3 - y + z = 2
STEP 2
Express the system in matrix form:
(-3/2 | 3 | 1
3 | -1 | 1
1/3 | -1 | 1)(x
y
z) = (2
5
2)
STEP 3
Write the system in augmented matrix form and use Gaussian elimination:
(-3/2 | 3 | 1 | 2
3 | -1 | 1 | 5
1/3 | -1 | 1 | 2)
STEP 4
Swap row 1 with row 2:
(3 | -1 | 1 | 5
-3/2 | 3 | 1 | 2
1/3 | -1 | 1 | 2)
STEP 5
Add 1/2 × (row 1) to row 2:
(3 | -1 | 1 | 5
0 | 5/2 | 3/2 | 9/2
1/3 | -1 | 1 | 2)
STEP 6
Multiply row 2 by 2:
(3 | -1 | 1 | 5
0 | 5 | 3 | 9
1/3 | -1 | 1 | 2)
STEP 7
Multiply row 3 by 3:
(3 | -1 | 1 | 5
0 | 5 | 3 | 9
1 | -3 | 3 | 6)
STEP 8
Subtract 1/3 × (row 1) from row 3:
(3 | -1 | 1 | 5
0 | 5 | 3 | 9
0 | -8/3 | 8/3 | 13/3)
STEP 9
Multiply row 3 by 3:
(3 | -1 | 1 | 5
0 | 5 | 3 | 9
0 | -8 | 8 | 13)
STEP 10
Swap row 2 with row 3:
(3 | -1 | 1 | 5
0 | -8 | 8 | 13
0 | 5 | 3 | 9)
STEP 11
Add 5/8 × (row 2) to row 3:
(3 | -1 | 1 | 5
0 | -8 | 8 | 13
0 | 0 | 8 | 137/8)
STEP 12
Multiply row 3 by 8:
(3 | -1 | 1 | 5
0 | -8 | 8 | 13
0 | 0 | 64 | 137)
STEP 13
Divide row 3 by 64:
(3 | -1 | 1 | 5
0 | -8 | 8 | 13
0 | 0 | 1 | 137/64)
STEP 14
Subtract 8 × (row 3) from row 2:
(3 | -1 | 1 | 5
0 | -8 | 0 | -33/8
0 | 0 | 1 | 137/64)
STEP 15
Divide row 2 by -8:
(3 | -1 | 1 | 5
0 | 1 | 0 | 33/64
0 | 0 | 1 | 137/64)
STEP 16
Add row 2 to row 1:
(3 | 0 | 1 | 353/64
0 | 1 | 0 | 33/64
0 | 0 | 1 | 137/64)
STEP 17
Subtract row 3 from row 1:
(3 | 0 | 0 | 27/8
0 | 1 | 0 | 33/64
0 | 0 | 1 | 137/64)
STEP 18
Divide row 1 by 3:
(1 | 0 | 0 | 9/8
0 | 1 | 0 | 33/64
0 | 0 | 1 | 137/64)
STEP 19
Collect results:
Answer: | 
 | {x = 9/8
y = 33/64
z = 137/64