x+y+z=2

2x-y+5z= -5

-x-2y+2z=1

# x+y+z=2, 2x-y+5z=-5,-x-2y+2z=1

x+y+z=2 <= eq1

2x-y+5z= -5 <= eq2

-x-2y+2z=1
<= eq3

eq1 + eq2
x + y + z = 2 add to  2x - y + 5z = - 5

3x + 6z = - 3
x + 2z = -1 <= eq4

eq1 + eq3
x + y + z = 2 add to  - x - 2y + 2z = 1
y + 3z = 3 <= eq5

in eq4 : x = - 1 - 2z <= 6

eq6 subtitute to eq3

- x -2y+2z = 1 <= eq3
-(-1 - 2z) - 2y + 2z = 1
1 + 2z - 2y + 2z = 1
- 2y + 4z = 0
4z = 2y
2z = y

z = y/2 < eq7

eq7 in eq5
y + 3z = 3 <= eq5
y + 3(y/2) = 3
2y + 3y = 3(2)
5y = 6

y = 6/5

y in eq2
2x-y+5z= -5 <= eq2
2x - (6/5) + 5z = - 5
2x - (6/5) + 5z + 5 = 0
10x - 6 + 5(5)z + 5(5) = 0
10x + 25z +25  - 6 = 0
10x + 25z = -19 <eq8

x + 2z = -1  <= eq4
x = - 2z - 1 <= x into eq8

10(-2z - 1) + 25z = -19
- 20z + 10 + 25z = -19
+ 10 + 5z = -19
5z = - 19 - 10
5z = - 29

z = -29/5

What we have computed  y = 6/5; z = -29/5 enter into eq1

x+y+z=2 <= eq1
x + (6/5) + (-29/5) = 2
x + (6/5) + (-29/5) - 2  = 0
[(5)x + 6 - 29 -(5)2] = 0
5x + 6 - 29 - 10 = 0
5x - 33 = 0
5x = 33

x = 33/5

Summary:   x = 33/5 : y = 6/5: z = -29/5 ◄ Ans

answered Oct 31, 2011 by Level 3 User (2,700 points)

# x+y+z=2, 2x-y+5z=-5,-x-2y+2z=1

x+y+z=2 <= eq1

2x-y+5z= -5 <= eq2

-x-2y+2z=1
<= eq3

eq1 + eq2
x + y + z = 2 add to  2x - y + 5z = - 5

3x + 6z = - 3
x + 2z = -1 <= eq4

eq1 + eq3
x + y + z = 2 add to  - x - 2y + 2z = 1
y + 3z = 3 <= eq5

in eq4 : x = - 1 - 2z <= 6

eq6 subtitute to eq3

- x -2y+2z = 1 <= eq3
-(-1 - 2z) - 2y + 2z = 1
1 + 2z - 2y + 2z = 1
- 2y + 4z = 0
4z = 2y
2z = y

z = y/2 < eq7

eq7 in eq5
y + 3z = 3 <= eq5
y + 3(y/2) = 3
2y + 3y = 3(2)
5y = 6

y = 6/5

y in eq2
2x-y+5z= -5 <= eq2
2x - (6/5) + 5z = - 5
2x - (6/5) + 5z + 5 = 0
10x - 6 + 5(5)z + 5(5) = 0
10x + 25z +25  - 6 = 0
10x + 25z = -19 <eq8

x + 2z = -1  <= eq4
x = - 2z - 1 <= x into eq8

10(-2z - 1) + 25z = -19

correction

- 20z - 10 + 25z = -19
- 10 + 5z = -19
5z = - 19 + 10
5z = - 9

z = - 9/5

What we have computed  y = 6/5; z = -29/5 enter into eq1

x+y+z=2 <= eq1
x + (6/5) + (-9/5) = 2
x + (6/5) + (-9/5) - 2  = 0
x + 6/5 - 9/5  - 2  = 0
[(5)x + 6  - 9  - (5)2] = 0

5x + 6 - 9 - 10 = 0
5x - 3 = 0
5x = 3

x = 3/5