Answer:
x = -1
, y = 4
, z = -3
Step-by-step explanation:
Solve the following system:
{-x + 3 y - 2 z = 19 | (equation 1)
2 x + y - z = 5 | (equation 2)
-3 x - y + 2 z = -7 | (equation 3)
Swap equation 1 with equation 3:
{-(3 x) - y + 2 z = -7 | (equation 1)
2 x + y - z = 5 | (equation 2)
-x + 3 y - 2 z = 19 | (equation 3)
Add 2/3 × (equation 1) to equation 2:
{-(3 x) - y + 2 z = -7 | (equation 1)
0 x+y/3 + z/3 = 1/3 | (equation 2)
-x + 3 y - 2 z = 19 | (equation 3)
Multiply equation 2 by 3:
{-(3 x) - y + 2 z = -7 | (equation 1)
0 x+y + z = 1 | (equation 2)
-x + 3 y - 2 z = 19 | (equation 3)
Subtract 1/3 × (equation 1) from equation 3:
{-(3 x) - y + 2 z = -7 | (equation 1)
0 x+y + z = 1 | (equation 2)
0 x+(10 y)/3 - (8 z)/3 = 64/3 | (equation 3)
Multiply equation 3 by 3/2:
{-(3 x) - y + 2 z = -7 | (equation 1)
0 x+y + z = 1 | (equation 2)
0 x+5 y - 4 z = 32 | (equation 3)
Swap equation 2 with equation 3:
{-(3 x) - y + 2 z = -7 | (equation 1)
0 x+5 y - 4 z = 32 | (equation 2)
0 x+y + z = 1 | (equation 3)
Subtract 1/5 × (equation 2) from equation 3:
{-(3 x) - y + 2 z = -7 | (equation 1)
0 x+5 y - 4 z = 32 | (equation 2)
0 x+0 y+(9 z)/5 = (-27)/5 | (equation 3)
Multiply equation 3 by 5/9:
{-(3 x) - y + 2 z = -7 | (equation 1)
0 x+5 y - 4 z = 32 | (equation 2)
0 x+0 y+z = -3 | (equation 3)
Add 4 × (equation 3) to equation 2:
{-(3 x) - y + 2 z = -7 | (equation 1)
0 x+5 y+0 z = 20 | (equation 2)
0 x+0 y+z = -3 | (equation 3)
Divide equation 2 by 5:
{-(3 x) - y + 2 z = -7 | (equation 1)
0 x+y+0 z = 4 | (equation 2)
0 x+0 y+z = -3 | (equation 3)
Add equation 2 to equation 1:
{-(3 x) + 0 y+2 z = -3 | (equation 1)
0 x+y+0 z = 4 | (equation 2)
0 x+0 y+z = -3 | (equation 3)
Subtract 2 × (equation 3) from equation 1:
{-(3 x)+0 y+0 z = 3 | (equation 1)
0 x+y+0 z = 4 | (equation 2)
0 x+0 y+z = -3 | (equation 3)
Divide equation 1 by -3:
{x+0 y+0 z = -1 | (equation 1)
0 x+y+0 z = 4 | (equation 2)
0 x+0 y+z = -3 | (equation 3)
Collect results:
Answer: {x = -1
, y = 4
, z = -3
