Problem to solve
Solve \[\frac{2x}{3}-2z=-2\], \[2y-4z=2\], \[\frac{x}{3}-5y=2\]
Solution
STEP 1
Solve the following system:
{-2 z + (2 x)/3 = -2 | (equation 1)
-4 z + 2 y = 2 | (equation 2)
-5 y + x/3 = 2 | (equation 3)
STEP 2
Multiply equation 1 by 3/2:
{x + 0 y - 3 z = -3 | (equation 1)
0 x+2 y - 4 z = 2 | (equation 2)
x/3 - 5 y+0 z = 2 | (equation 3)
STEP 3
Divide equation 2 by 2:
{x + 0 y - 3 z = -3 | (equation 1)
0 x+y - 2 z = 1 | (equation 2)
x/3 - 5 y+0 z = 2 | (equation 3)
STEP 4
Multiply equation 3 by 3:
{x + 0 y - 3 z = -3 | (equation 1)
0 x+y - 2 z = 1 | (equation 2)
x - 15 y+0 z = 6 | (equation 3)
STEP 5
Subtract equation 1 from equation 3:
{x + 0 y - 3 z = -3 | (equation 1)
0 x+y - 2 z = 1 | (equation 2)
0 x - 15 y + 3 z = 9 | (equation 3)
STEP 6
Divide equation 3 by 3:
{x + 0 y - 3 z = -3 | (equation 1)
0 x+y - 2 z = 1 | (equation 2)
0 x - 5 y + z = 3 | (equation 3)
STEP 7
Swap equation 2 with equation 3:
{x + 0 y - 3 z = -3 | (equation 1)
0 x - 5 y + z = 3 | (equation 2)
0 x+y - 2 z = 1 | (equation 3)
STEP 8
Add 1/5 × (equation 2) to equation 3:
{x + 0 y - 3 z = -3 | (equation 1)
0 x - 5 y + z = 3 | (equation 2)
0 x+0 y - (9 z)/5 = 8/5 | (equation 3)
STEP 9
Multiply equation 3 by 5:
{x + 0 y - 3 z = -3 | (equation 1)
0 x - 5 y + z = 3 | (equation 2)
0 x+0 y - 9 z = 8 | (equation 3)
STEP 10
Divide equation 3 by -9:
{x + 0 y - 3 z = -3 | (equation 1)
0 x - 5 y + z = 3 | (equation 2)
0 x+0 y+z = -8/9 | (equation 3)
STEP 11
Subtract equation 3 from equation 2:
{x + 0 y - 3 z = -3 | (equation 1)
0 x - 5 y+0 z = 35/9 | (equation 2)
0 x+0 y+z = -8/9 | (equation 3)
STEP 12
Divide equation 2 by -5:
{x + 0 y - 3 z = -3 | (equation 1)
0 x+y+0 z = -7/9 | (equation 2)
0 x+0 y+z = -8/9 | (equation 3)
STEP 13
Add 3 × (equation 3) to equation 1:
{x+0 y+0 z = -17/3 | (equation 1)
0 x+y+0 z = -7/9 | (equation 2)
0 x+0 y+z = -8/9 | (equation 3)
STEP 14
Collect results:
Answer: | 
 | {x = -17/3
y = -7/9
z = -8/9