Answer:
x = -125/71
, y = 448/71
, z = 356/71
Step-by-step explanation:
Solve the following system:
{2 x - 5 y + 5 z = -10 | (equation 1)
5 x - 4 y + 3 z = -19 | (equation 2)
x - y + 5 z = 17 | (equation 3)
Swap equation 1 with equation 2:
{5 x - 4 y + 3 z = -19 | (equation 1)
2 x - 5 y + 5 z = -10 | (equation 2)
x - y + 5 z = 17 | (equation 3)
Subtract 2/5 × (equation 1) from equation 2:
{5 x - 4 y + 3 z = -19 | (equation 1)
0 x - (17 y)/5 + (19 z)/5 = (-12)/5 | (equation 2)
x - y + 5 z = 17 | (equation 3)
Multiply equation 2 by 5:
{5 x - 4 y + 3 z = -19 | (equation 1)
0 x - 17 y + 19 z = -12 | (equation 2)
x - y + 5 z = 17 | (equation 3)
Subtract 1/5 × (equation 1) from equation 3:
{5 x - 4 y + 3 z = -19 | (equation 1)
0 x - 17 y + 19 z = -12 | (equation 2)
0 x - y/5 + (22 z)/5 = 104/5 | (equation 3)
Multiply equation 3 by 5:
{5 x - 4 y + 3 z = -19 | (equation 1)
0 x - 17 y + 19 z = -12 | (equation 2)
0 x - y + 22 z = 104 | (equation 3)
Subtract 1/17 × (equation 2) from equation 3:
{5 x - 4 y + 3 z = -19 | (equation 1)
0 x - 17 y + 19 z = -12 | (equation 2)
0 x+0 y+(355 z)/17 = 1780/17 | (equation 3)
Multiply equation 3 by 17/5:
{5 x - 4 y + 3 z = -19 | (equation 1)
0 x - 17 y + 19 z = -12 | (equation 2)
0 x+0 y+71 z = 356 | (equation 3)
Divide equation 3 by 71:
{5 x - 4 y + 3 z = -19 | (equation 1)
0 x - 17 y + 19 z = -12 | (equation 2)
0 x+0 y+z = 356/71 | (equation 3)
Subtract 19 × (equation 3) from equation 2:
{5 x - 4 y + 3 z = -19 | (equation 1)
0 x - 17 y+0 z = (-7616)/71 | (equation 2)
0 x+0 y+z = 356/71 | (equation 3)
Divide equation 2 by -17:
{5 x - 4 y + 3 z = -19 | (equation 1)
0 x+y+0 z = 448/71 | (equation 2)
0 x+0 y+z = 356/71 | (equation 3)
Add 4 × (equation 2) to equation 1:
{5 x + 0 y+3 z = 443/71 | (equation 1)
0 x+y+0 z = 448/71 | (equation 2)
0 x+0 y+z = 356/71 | (equation 3)
Subtract 3 × (equation 3) from equation 1:
{5 x+0 y+0 z = (-625)/71 | (equation 1)
0 x+y+0 z = 448/71 | (equation 2)
0 x+0 y+z = 356/71 | (equation 3)
Divide equation 1 by 5:
{x+0 y+0 z = (-125)/71 | (equation 1)
0 x+y+0 z = 448/71 | (equation 2)
0 x+0 y+z = 356/71 | (equation 3)
Collect results:
Answer: {x = -125/71
, y = 448/71
, z = 356/71
, 
, thus
.