Answer:
x = 2
, y = 5
, z = -1
Step-by-step explanation:
Solve the following system:
{9 x + 3 y - 4 z = 37 | (equation 1)
4 x + 3 y + 7 z = 16 | (equation 2)
x - 5 y + 8 z = -31 | (equation 3)
Subtract 4/9 × (equation 1) from equation 2:
{9 x + 3 y - 4 z = 37 | (equation 1)
0 x+(5 y)/3 + (79 z)/9 = -4/9 | (equation 2)
x - 5 y + 8 z = -31 | (equation 3)
Multiply equation 2 by 9:
{9 x + 3 y - 4 z = 37 | (equation 1)
0 x+15 y + 79 z = -4 | (equation 2)
x - 5 y + 8 z = -31 | (equation 3)
Subtract 1/9 × (equation 1) from equation 3:
{9 x + 3 y - 4 z = 37 | (equation 1)
0 x+15 y + 79 z = -4 | (equation 2)
0 x - (16 y)/3 + (76 z)/9 = -316/9 | (equation 3)
Multiply equation 3 by 9/4:
{9 x + 3 y - 4 z = 37 | (equation 1)
0 x+15 y + 79 z = -4 | (equation 2)
0 x - 12 y + 19 z = -79 | (equation 3)
Add 4/5 × (equation 2) to equation 3:
{9 x + 3 y - 4 z = 37 | (equation 1)
0 x+15 y + 79 z = -4 | (equation 2)
0 x+0 y+(411 z)/5 = -411/5 | (equation 3)
Multiply equation 3 by 5/411:
{9 x + 3 y - 4 z = 37 | (equation 1)
0 x+15 y + 79 z = -4 | (equation 2)
0 x+0 y+z = -1 | (equation 3)
Subtract 79 × (equation 3) from equation 2:
{9 x + 3 y - 4 z = 37 | (equation 1)
0 x+15 y+0 z = 75 | (equation 2)
0 x+0 y+z = -1 | (equation 3)
Divide equation 2 by 15:
{9 x + 3 y - 4 z = 37 | (equation 1)
0 x+y+0 z = 5 | (equation 2)
0 x+0 y+z = -1 | (equation 3)
Subtract 3 × (equation 2) from equation 1:
{9 x + 0 y - 4 z = 22 | (equation 1)
0 x+y+0 z = 5 | (equation 2)
0 x+0 y+z = -1 | (equation 3)
Add 4 × (equation 3) to equation 1:
{9 x+0 y+0 z = 18 | (equation 1)
0 x+y+0 z = 5 | (equation 2)
0 x+0 y+z = -1 | (equation 3)
Divide equation 1 by 9:
{x+0 y+0 z = 2 | (equation 1)
0 x+y+0 z = 5 | (equation 2)
0 x+0 y+z = -1 | (equation 3)
Collect results:
Answer: {x = 2
, y = 5
, z = -1
