Answer:
x = -2 , y = -3 , z = 3
Step-by-step explanation:
Solve the following system:
{-x - 5 y - 5 z = 2 | (equation 1)
4 x - 5 y + 4 z = 19 | (equation 2)
x + 5 y - z = -20 | (equation 3)
Swap equation 1 with equation 2:
{4 x - 5 y + 4 z = 19 | (equation 1)
-x - 5 y - 5 z = 2 | (equation 2)
x + 5 y - z = -20 | (equation 3)
Add 1/4 × (equation 1) to equation 2:
{4 x - 5 y + 4 z = 19 | (equation 1)
0 x - (25 y)/4 - 4 z = 27/4 | (equation 2)
x + 5 y - z = -20 | (equation 3)
Multiply equation 2 by 4:
{4 x - 5 y + 4 z = 19 | (equation 1)
0 x - 25 y - 16 z = 27 | (equation 2)
x + 5 y - z = -20 | (equation 3)
Subtract 1/4 × (equation 1) from equation 3:
{4 x - 5 y + 4 z = 19 | (equation 1)
0 x - 25 y - 16 z = 27 | (equation 2)
0 x+(25 y)/4 - 2 z = -99/4 | (equation 3)
Multiply equation 3 by 4:
{4 x - 5 y + 4 z = 19 | (equation 1)
0 x - 25 y - 16 z = 27 | (equation 2)
0 x+25 y - 8 z = -99 | (equation 3)
Add equation 2 to equation 3:
{4 x - 5 y + 4 z = 19 | (equation 1)
0 x - 25 y - 16 z = 27 | (equation 2)
0 x+0 y - 24 z = -72 | (equation 3)
Divide equation 3 by -24:
{4 x - 5 y + 4 z = 19 | (equation 1)
0 x - 25 y - 16 z = 27 | (equation 2)
0 x+0 y+z = 3 | (equation 3)
Add 16 × (equation 3) to equation 2:
{4 x - 5 y + 4 z = 19 | (equation 1)
0 x - 25 y+0 z = 75 | (equation 2)
0 x+0 y+z = 3 | (equation 3)
Divide equation 2 by -25:
{4 x - 5 y + 4 z = 19 | (equation 1)
0 x+y+0 z = -3 | (equation 2)
0 x+0 y+z = 3 | (equation 3)
Add 5 × (equation 2) to equation 1:
{4 x + 0 y+4 z = 4 | (equation 1)
0 x+y+0 z = -3 | (equation 2)
0 x+0 y+z = 3 | (equation 3)
Subtract 4 × (equation 3) from equation 1:
{4 x+0 y+0 z = -8 | (equation 1)
0 x+y+0 z = -3 | (equation 2)
0 x+0 y+z = 3 | (equation 3)
Divide equation 1 by 4:
{x+0 y+0 z = -2 | (equation 1)
0 x+y+0 z = -3 | (equation 2)
0 x+0 y+z = 3 | (equation 3)
Collect results:
Answer: {x = -2 , y = -3 , z = 3
