2x-5y+5z=-10

5x-4y+3z=-19

X-y+5z=17

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