-x+y+6z=? You did not spcify so I just made it 0
x = -22/5, y = -4/5, z = -3/5
Step-by-step explanation:
Solve the following system:
{-x - 3 y - 2 z = 8 | (equation 1)
-x + y + 6 z = 0 | (equation 2)
x - 9 y - 2 z = 4 | (equation 3)
Subtract equation 1 from equation 2:
{-x - 3 y - 2 z = 8 | (equation 1)
0 x+4 y + 8 z = -8 | (equation 2)
x - 9 y - 2 z = 4 | (equation 3)
Divide equation 2 by 4:
{-x - 3 y - 2 z = 8 | (equation 1)
0 x+y + 2 z = -2 | (equation 2)
x - 9 y - 2 z = 4 | (equation 3)
Add equation 1 to equation 3:
{-x - 3 y - 2 z = 8 | (equation 1)
0 x+y + 2 z = -2 | (equation 2)
0 x - 12 y - 4 z = 12 | (equation 3)
Divide equation 3 by 4:
{-x - 3 y - 2 z = 8 | (equation 1)
0 x+y + 2 z = -2 | (equation 2)
0 x - 3 y - z = 3 | (equation 3)
Swap equation 2 with equation 3:
{-x - 3 y - 2 z = 8 | (equation 1)
0 x - 3 y - z = 3 | (equation 2)
0 x+y + 2 z = -2 | (equation 3)
Add 1/3 × (equation 2) to equation 3:
{-x - 3 y - 2 z = 8 | (equation 1)
0 x - 3 y - z = 3 | (equation 2)
0 x+0 y+(5 z)/3 = -1 | (equation 3)
Multiply equation 3 by 3:
{-x - 3 y - 2 z = 8 | (equation 1)
0 x - 3 y - z = 3 | (equation 2)
0 x+0 y+5 z = -3 | (equation 3)
Divide equation 3 by 5:
{-x - 3 y - 2 z = 8 | (equation 1)
0 x - 3 y - z = 3 | (equation 2)
0 x+0 y+z = -3/5 | (equation 3)
Add equation 3 to equation 2:
{-x - 3 y - 2 z = 8 | (equation 1)
0 x - 3 y+0 z = 12/5 | (equation 2)
0 x+0 y+z = -3/5 | (equation 3)
Divide equation 2 by -3:
{-x - 3 y - 2 z = 8 | (equation 1)
0 x+y+0 z = -4/5 | (equation 2)
0 x+0 y+z = -3/5 | (equation 3)
Add 3 × (equation 2) to equation 1:
{-x + 0 y - 2 z = 28/5 | (equation 1)
0 x+y+0 z = -4/5 | (equation 2)
0 x+0 y+z = -3/5 | (equation 3)
Add 2 × (equation 3) to equation 1:
{-x+0 y+0 z = 22/5 | (equation 1)
0 x+y+0 z = -4/5 | (equation 2)
0 x+0 y+z = -3/5 | (equation 3)
Multiply equation 1 by -1:
{x+0 y+0 z = -22/5 | (equation 1)
0 x+y+0 z = -4/5 | (equation 2)
0 x+0 y+z = -3/5 | (equation 3)
Collect results:
{x = -22/5, y = -4/5, z = -3/5
