Answer:
x = 1, y = -4, z = -5
Explanation:
Solve the following system:
{x = -4 z - 19 | (equation 1)
{y = z + 5 x - 4 | (equation 2)
{-z - 5 y = 25 | (equation 3)
Express the system in standard form:
{x + 0 y + 4 z = -19 | (equation 1)
{-(5 x) + y - z = -4 | (equation 2)
{0 x - 5 y - z = 25 | (equation 3)
Swap equation 1 with equation 2:
{-(5 x) + y - z = -4 | (equation 1)
{x + 0 y + 4 z = -19 | (equation 2)
{0 x - 5 y - z = 25 | (equation 3)
Add 1/5 × (equation 1) to equation 2:
{-(5 x) + y - z = -4 | (equation 1)
{0 x + y/5 + (19 z)/5 = -99/5 | (equation 2)
{0 x - 5 y - z = 25 | (equation 3)
Multiply equation 2 by 5:
{-(5 x) + y - z = -4 | (equation 1)
{0 x + y + 19 z = -99 | (equation 2)
{0 x - 5 y - z = 25 | (equation 3)
Swap equation 2 with equation 3:
{-(5 x) + y - z = -4 | (equation 1)
{0 x - 5 y - z = 25 | (equation 2)
{0 x + y + 19 z = -99 | (equation 3)
Add 1/5 × (equation 2) to equation 3:
{-(5 x) + y - z = -4 | (equation 1)
{0 x - 5 y - z = 25 | (equation 2)
{0 x + 0 y + (94 z)/5 = -94 | (equation 3)
Multiply equation 3 by 5/94:
{-(5 x) + y - z = -4 | (equation 1)
{0 x - 5 y - z = 25 | (equation 2)
{0 x + 0 y + z = -5 | (equation 3)
Add equation 3 to equation 2:
{-(5 x) + y - z = -4 | (equation 1)
{0 x - 5 y + 0 z = 20 | (equation 2)
{0 x + 0 y + z = -5 | (equation 3)
Divide equation 2 by -5:
{-(5 x) + y - z = -4 | (equation 1)
{0 x + y + 0 z = -4 | (equation 2)
{0 x + 0 y + z = -5 | (equation 3)
Subtract equation 2 from equation 1:
{-(5 x) + 0 y - z = 0 | (equation 1)
{0 x + y + 0 z = -4 | (equation 2)
{0 x + 0 y + z = -5 | (equation 3)
Add equation 3 to equation 1:
{-(5 x) + 0 y + 0 z = -5 | (equation 1)
{0 x + y + 0 z = -4 | (equation 2)
{0 x + 0 y + z = -5 | (equation 3)
Divide equation 1 by -5:
{x + 0 y + 0 z = 1 | (equation 1)
{0 x + y + 0 z = -4 | (equation 2)
{0 x + 0 y + z = -5 | (equation 3)
Collect results:
Answer: {x = 1, y = -4, z = -5