B:) x = 1
, y = 6
, z = -6
Step-by-step explanation:
Solve the following system:
{3 x + 4 y + 3 z = 9 | (equation 1)
3 x + 3 y + 3 z = 3 | (equation 2)
2 x + 4 y + 3 z = 8 | (equation 3)
Subtract equation 1 from equation 2:
{3 x + 4 y + 3 z = 9 | (equation 1)
0 x - y+0 z = -6 | (equation 2)
2 x + 4 y + 3 z = 8 | (equation 3)
Multiply equation 2 by -1:
{3 x + 4 y + 3 z = 9 | (equation 1)
0 x+y+0 z = 6 | (equation 2)
2 x + 4 y + 3 z = 8 | (equation 3)
Subtract 2/3 × (equation 1) from equation 3:
{3 x + 4 y + 3 z = 9 | (equation 1)
0 x+y+0 z = 6 | (equation 2)
0 x+(4 y)/3 + z = 2 | (equation 3)
Multiply equation 3 by 3:
{3 x + 4 y + 3 z = 9 | (equation 1)
0 x+y+0 z = 6 | (equation 2)
0 x+4 y + 3 z = 6 | (equation 3)
Swap equation 2 with equation 3:
{3 x + 4 y + 3 z = 9 | (equation 1)
0 x+4 y + 3 z = 6 | (equation 2)
0 x+y+0 z = 6 | (equation 3)
Subtract 1/4 × (equation 2) from equation 3:
{3 x + 4 y + 3 z = 9 | (equation 1)
0 x+4 y + 3 z = 6 | (equation 2)
0 x+0 y - (3 z)/4 = 9/2 | (equation 3)
Multiply equation 3 by 4/3:
{3 x + 4 y + 3 z = 9 | (equation 1)
0 x+4 y + 3 z = 6 | (equation 2)
0 x+0 y - z = 6 | (equation 3)
Multiply equation 3 by -1:
{3 x + 4 y + 3 z = 9 | (equation 1)
0 x+4 y + 3 z = 6 | (equation 2)
0 x+0 y+z = -6 | (equation 3)
Subtract 3 × (equation 3) from equation 2:
{3 x + 4 y + 3 z = 9 | (equation 1)
0 x+4 y+0 z = 24 | (equation 2)
0 x+0 y+z = -6 | (equation 3)
Divide equation 2 by 4:
{3 x + 4 y + 3 z = 9 | (equation 1)
0 x+y+0 z = 6 | (equation 2)
0 x+0 y+z = -6 | (equation 3)
Subtract 4 × (equation 2) from equation 1:
{3 x + 0 y+3 z = -15 | (equation 1)
0 x+y+0 z = 6 | (equation 2)
0 x+0 y+z = -6 | (equation 3)
Subtract 3 × (equation 3) from equation 1:
{3 x+0 y+0 z = 3 | (equation 1)
0 x+y+0 z = 6 | (equation 2)
0 x+0 y+z = -6 | (equation 3)
Divide equation 1 by 3:
{x+0 y+0 z = 1 | (equation 1)
0 x+y+0 z = 6 | (equation 2)
0 x+0 y+z = -6 | (equation 3)
Collect results:
{x = 1
, y = 6
, z = -6
