Answer:
{x = -4 , y = 2 , z = 1
Explanation:
Solve the following system:
{-2 x + y + 2 z = 12 | (equation 1)
2 x - 4 y + z = -15 | (equation 2)
y + 4 z = 6 | (equation 3)
Add equation 1 to equation 2:
{-(2 x) + y + 2 z = 12 | (equation 1)
0 x - 3 y + 3 z = -3 | (equation 2)
0 x+y + 4 z = 6 | (equation 3)
Divide equation 2 by 3:
{-(2 x) + y + 2 z = 12 | (equation 1)
0 x - y + z = -1 | (equation 2)
0 x+y + 4 z = 6 | (equation 3)
Add equation 2 to equation 3:
{-(2 x) + y + 2 z = 12 | (equation 1)
0 x - y + z = -1 | (equation 2)
0 x+0 y+5 z = 5 | (equation 3)
Divide equation 3 by 5:
{-(2 x) + y + 2 z = 12 | (equation 1)
0 x - y + z = -1 | (equation 2)
0 x+0 y+z = 1 | (equation 3)
Subtract equation 3 from equation 2:
{-(2 x) + y + 2 z = 12 | (equation 1)
0 x - y+0 z = -2 | (equation 2)
0 x+0 y+z = 1 | (equation 3)
Multiply equation 2 by -1:
{-(2 x) + y + 2 z = 12 | (equation 1)
0 x+y+0 z = 2 | (equation 2)
0 x+0 y+z = 1 | (equation 3)
Subtract equation 2 from equation 1:
{-(2 x) + 0 y+2 z = 10 | (equation 1)
0 x+y+0 z = 2 | (equation 2)
0 x+0 y+z = 1 | (equation 3)
Subtract 2 × (equation 3) from equation 1:
{-(2 x)+0 y+0 z = 8 | (equation 1)
0 x+y+0 z = 2 | (equation 2)
0 x+0 y+z = 1 | (equation 3)
Divide equation 1 by -2:
{x+0 y+0 z = -4 | (equation 1)
0 x+y+0 z = 2 | (equation 2)
0 x+0 y+z = 1 | (equation 3)
Collect results:
Answer: {x = -4 , y = 2 , z = 1