Answer:
x = 0
, y = 1
, z = 3
Step-by-step explanation:
Solve the following system:
{5 x + 4 y - z = 1 | (equation 1)
2 x - 2 y + z = 1 | (equation 2)
-x - y + z = 2 | (equation 3)
Subtract 2/5 × (equation 1) from equation 2:
{5 x + 4 y - z = 1 | (equation 1)
0 x - (18 y)/5 + (7 z)/5 = 3/5 | (equation 2)
-x - y + z = 2 | (equation 3)
Multiply equation 2 by 5:
{5 x + 4 y - z = 1 | (equation 1)
0 x - 18 y + 7 z = 3 | (equation 2)
-x - y + z = 2 | (equation 3)
Add 1/5 × (equation 1) to equation 3:
{5 x + 4 y - z = 1 | (equation 1)
0 x - 18 y + 7 z = 3 | (equation 2)
0 x - y/5 + (4 z)/5 = 11/5 | (equation 3)
Multiply equation 3 by 5:
{5 x + 4 y - z = 1 | (equation 1)
0 x - 18 y + 7 z = 3 | (equation 2)
0 x - y + 4 z = 11 | (equation 3)
Subtract 1/18 × (equation 2) from equation 3:
{5 x + 4 y - z = 1 | (equation 1)
0 x - 18 y + 7 z = 3 | (equation 2)
0 x+0 y+(65 z)/18 = 65/6 | (equation 3)
Multiply equation 3 by 18/65:
{5 x + 4 y - z = 1 | (equation 1)
0 x - 18 y + 7 z = 3 | (equation 2)
0 x+0 y+z = 3 | (equation 3)
Subtract 7 × (equation 3) from equation 2:
{5 x + 4 y - z = 1 | (equation 1)
0 x - 18 y+0 z = -18 | (equation 2)
0 x+0 y+z = 3 | (equation 3)
Divide equation 2 by -18:
{5 x + 4 y - z = 1 | (equation 1)
0 x+y+0 z = 1 | (equation 2)
0 x+0 y+z = 3 | (equation 3)
Subtract 4 × (equation 2) from equation 1:
{5 x + 0 y - z = -3 | (equation 1)
0 x+y+0 z = 1 | (equation 2)
0 x+0 y+z = 3 | (equation 3)
Add equation 3 to equation 1:
{5 x+0 y+0 z = 0 | (equation 1)
0 x+y+0 z = 1 | (equation 2)
0 x+0 y+z = 3 | (equation 3)
Divide equation 1 by 5:
{x+0 y+0 z = 0 | (equation 1)
0 x+y+0 z = 1 | (equation 2)
0 x+0 y+z = 3 | (equation 3)
Collect results:
Answer: {x = 0
, y = 1
, z = 3
