Respuesta :
Answer:
x = 1 , y = 1 , z = 0
Step-by-step explanation by elimination:
Solve the following system:
{-2 x + 2 y + 3 z = 0 | (equation 1)
-2 x - y + z = -3 | (equation 2)
2 x + 3 y + 3 z = 5 | (equation 3)
Subtract equation 1 from equation 2:
{-(2 x) + 2 y + 3 z = 0 | (equation 1)
0 x - 3 y - 2 z = -3 | (equation 2)
2 x + 3 y + 3 z = 5 | (equation 3)
Multiply equation 2 by -1:
{-(2 x) + 2 y + 3 z = 0 | (equation 1)
0 x+3 y + 2 z = 3 | (equation 2)
2 x + 3 y + 3 z = 5 | (equation 3)
Add equation 1 to equation 3:
{-(2 x) + 2 y + 3 z = 0 | (equation 1)
0 x+3 y + 2 z = 3 | (equation 2)
0 x+5 y + 6 z = 5 | (equation 3)
Swap equation 2 with equation 3:
{-(2 x) + 2 y + 3 z = 0 | (equation 1)
0 x+5 y + 6 z = 5 | (equation 2)
0 x+3 y + 2 z = 3 | (equation 3)
Subtract 3/5 × (equation 2) from equation 3:
{-(2 x) + 2 y + 3 z = 0 | (equation 1)
0 x+5 y + 6 z = 5 | (equation 2)
0 x+0 y - (8 z)/5 = 0 | (equation 3)
Multiply equation 3 by 5/8:
{-(2 x) + 2 y + 3 z = 0 | (equation 1)
0 x+5 y + 6 z = 5 | (equation 2)
0 x+0 y - z = 0 | (equation 3)
Multiply equation 3 by -1:
{-(2 x) + 2 y + 3 z = 0 | (equation 1)
0 x+5 y + 6 z = 5 | (equation 2)
0 x+0 y+z = 0 | (equation 3)
Subtract 6 × (equation 3) from equation 2:
{-(2 x) + 2 y + 3 z = 0 | (equation 1)
0 x+5 y+0 z = 5 | (equation 2)
0 x+0 y+z = 0 | (equation 3)
Divide equation 2 by 5:
{-(2 x) + 2 y + 3 z = 0 | (equation 1)
0 x+y+0 z = 1 | (equation 2)
0 x+0 y+z = 0 | (equation 3)
Subtract 2 × (equation 2) from equation 1:
{-(2 x) + 0 y+3 z = -2 | (equation 1)
0 x+y+0 z = 1 | (equation 2)
0 x+0 y+z = 0 | (equation 3)
Subtract 3 × (equation 3) from equation 1:
{-(2 x)+0 y+0 z = -2 | (equation 1)
0 x+y+0 z = 1 | (equation 2)
0 x+0 y+z = 0 | (equation 3)
Divide equation 1 by -2:
{x+0 y+0 z = 1 | (equation 1)
0 x+y+0 z = 1 | (equation 2)
0 x+0 y+z = 0 | (equation 3)
Collect results:
Answer: {x = 1 , y = 1 , z = 0
Answer:
x = 1 , y = 1 , z = 0
Step-by-step explanation:
Add first equation to third one
-2x + 2y + 3z = 0
+
2x + 3y + 3z = 5
----------------- -------
5y + 6z = 5 (4th equation)
Subtract second equation to first one
-2x + 2y + 3z = 0
-
-2x - y + z = -3
------------------ --------
3y + 2z = 3 (5th equation)
Multiply 5th equation by 3
3*(3y + 2z) = 3*3
9y + 6z = 9 (6th equation)
Subtract 6th equation to fourth one
5y + 6z = 5
-
9y + 6z = 9
-----------
-4y = -4
Solve for y
-4y = -4
y = (-4)/(-4)
y = 1
Replace this value in 4th equation and solve for z
5(1) + 6z = 5
6z = 5-5
6z = 0
z = 0
Replace y and z values obtained in first equation and solve for x
-2x + 2y + 3z = 0
-2x + 2(1) + 3(0) = 0
-2x + 2 = 0
-2x = -2
x = (-2)/(-2)
x = 1
