x = 17/3
, y = 1
, z = -4/3
Step-by-step explanation:
Solve the following system:
{2 x - 5 y + z = 5 | (equation 1)
-2 + 3 x + 2 y = 17 | (equation 2)
4 x - 3 y + 2 z = 17 | (equation 3)
Express the system in standard form:
{2 x - 5 y + z = 5 | (equation 1)
3 x + 2 y+0 z = 19 | (equation 2)
4 x - 3 y + 2 z = 17 | (equation 3)
Swap equation 1 with equation 3:
{4 x - 3 y + 2 z = 17 | (equation 1)
3 x + 2 y+0 z = 19 | (equation 2)
2 x - 5 y + z = 5 | (equation 3)
Subtract 3/4 × (equation 1) from equation 2:
{4 x - 3 y + 2 z = 17 | (equation 1)
0 x+(17 y)/4 - (3 z)/2 = 25/4 | (equation 2)
2 x - 5 y + z = 5 | (equation 3)
Multiply equation 2 by 4:
{4 x - 3 y + 2 z = 17 | (equation 1)
0 x+17 y - 6 z = 25 | (equation 2)
2 x - 5 y + z = 5 | (equation 3)
Subtract 1/2 × (equation 1) from equation 3:
{4 x - 3 y + 2 z = 17 | (equation 1)
0 x+17 y - 6 z = 25 | (equation 2)
0 x - (7 y)/2+0 z = (-7)/2 | (equation 3)
Multiply equation 3 by -2/7:
{4 x - 3 y + 2 z = 17 | (equation 1)
0 x+17 y - 6 z = 25 | (equation 2)
0 x+y+0 z = 1 | (equation 3)
Subtract 1/17 × (equation 2) from equation 3:
{4 x - 3 y + 2 z = 17 | (equation 1)
0 x+17 y - 6 z = 25 | (equation 2)
0 x+0 y+(6 z)/17 = (-8)/17 | (equation 3)
Multiply equation 3 by 17/2:
{4 x - 3 y + 2 z = 17 | (equation 1)
0 x+17 y - 6 z = 25 | (equation 2)
0 x+0 y+3 z = -4 | (equation 3)
Divide equation 3 by 3:
{4 x - 3 y + 2 z = 17 | (equation 1)
0 x+17 y - 6 z = 25 | (equation 2)
0 x+0 y+z = (-4)/3 | (equation 3)
Add 6 × (equation 3) to equation 2:
{4 x - 3 y + 2 z = 17 | (equation 1)
0 x+17 y+0 z = 17 | (equation 2)
0 x+0 y+z = -4/3 | (equation 3)
Divide equation 2 by 17:
{4 x - 3 y + 2 z = 17 | (equation 1)
0 x+y+0 z = 1 | (equation 2)
0 x+0 y+z = -4/3 | (equation 3)
Add 3 × (equation 2) to equation 1:
{4 x + 0 y+2 z = 20 | (equation 1)
0 x+y+0 z = 1 | (equation 2)
0 x+0 y+z = -4/3 | (equation 3)
Subtract 2 × (equation 3) from equation 1:
{4 x+0 y+0 z = 68/3 | (equation 1)
0 x+y+0 z = 1 | (equation 2)
0 x+0 y+z = -4/3 | (equation 3)
Divide equation 1 by 4:
{x+0 y+0 z = 17/3 | (equation 1)
0 x+y+0 z = 1 | (equation 2)
0 x+0 y+z = -4/3 | (equation 3)
Collect results:
{x = 17/3
, y = 1
, z = -4/3
