Answer:
x = 30/7 , y = 46/7 , z = 48/7
Explanation:
Solve the following system:
{2 x + 3 y - z = 5 x | (equation 1)
2 z - 3 y = -6 | (equation 2)
3 x + y - 4 z = -8 | (equation 3)
Express the system in standard form:
{-(3 x) + 3 y - z = 0 | (equation 1)
0 x - 3 y + 2 z = -6 | (equation 2)
3 x + y - 4 z = -8 | (equation 3)
Add equation 1 to equation 3:
{-(3 x) + 3 y - z = 0 | (equation 1)
0 x - 3 y + 2 z = -6 | (equation 2)
0 x+4 y - 5 z = -8 | (equation 3)
Swap equation 2 with equation 3:
{-(3 x) + 3 y - z = 0 | (equation 1)
0 x+4 y - 5 z = -8 | (equation 2)
0 x - 3 y + 2 z = -6 | (equation 3)
Add 3/4 × (equation 2) to equation 3:
{-(3 x) + 3 y - z = 0 | (equation 1)
0 x+4 y - 5 z = -8 | (equation 2)
0 x+0 y - (7 z)/4 = -12 | (equation 3)
Multiply equation 3 by -4:
{-(3 x) + 3 y - z = 0 | (equation 1)
0 x+4 y - 5 z = -8 | (equation 2)
0 x+0 y+7 z = 48 | (equation 3)
Divide equation 3 by 7:
{-(3 x) + 3 y - z = 0 | (equation 1)
0 x+4 y - 5 z = -8 | (equation 2)
0 x+0 y+z = 48/7 | (equation 3)
Add 5 × (equation 3) to equation 2:
{-(3 x) + 3 y - z = 0 | (equation 1)
0 x+4 y+0 z = 184/7 | (equation 2)
0 x+0 y+z = 48/7 | (equation 3)
Divide equation 2 by 4:
{-(3 x) + 3 y - z = 0 | (equation 1)
0 x+y+0 z = 46/7 | (equation 2)
0 x+0 y+z = 48/7 | (equation 3)
Subtract 3 × (equation 2) from equation 1:
{-(3 x) + 0 y - z = -138/7 | (equation 1)
0 x+y+0 z = 46/7 | (equation 2)
0 x+0 y+z = 48/7 | (equation 3)
Add equation 3 to equation 1:
{-(3 x)+0 y+0 z = -90/7 | (equation 1)
0 x+y+0 z = 46/7 | (equation 2)
0 x+0 y+z = 48/7 | (equation 3)
Divide equation 1 by -3:
{x+0 y+0 z = 30/7 | (equation 1)
0 x+y+0 z = 46/7 | (equation 2)
0 x+0 y+z = 48/7 | (equation 3)
Collect results:
Answer: {x = 30/7 , y = 46/7 , z = 48/7