What is x+y+z=6,x-y+z=2,x+2y-z=2 ?

The solution to x+y+z=6,x-y+z=2,x+2y-z=2 is x=1,y=2,z=3

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x+y+z=6,x-y+z=2,x+2y-z=2

x + y + z = 6, x - y + z = 2, x + 2 y - z = 2

x = 1, y = 2, z = 3

Solution steps

x + y + z = 6 x - y + z = 2 x + 2 y - z = 2

Isolate

x

for

x + y + z = 6 : x = 6 - y - z

Substitute

x = 6 - y - z

[6 - y - z - y + z = 2 6 - y - z + 2 y - z = 2]

Simplify

[- 2 y + 6 = 2 y - 2 z + 6 = 2]

Isolate

y

for

- 2 y + 6 = 2 : y = 2

Substitute

y = 2

[2 - 2 z + 6 = 2]

Simplify

[- 2 z + 8 = 2]

Isolate

z

for

- 2 z + 8 = 2 : z = 3

For

x = 6 - y - z

Substitute

y = 2, z = 3

x = 6 - 2 - 3

Simplify

x = 1

The solutions to the system of equations are:

x = 1, y = 2, z = 3

2 x - 3 y + 9 = 0, x + 2 y = - 1

x + 2 z = 1, y + z = 4

3 x + 4 y = - 18, 7 x - 6 y = 4

3 x^{2} + 2 x - k = 0, x = \frac{1}{3}

x + y = 4, 5 x - 2 y = 3

What is x+y+z=6,x-y+z=2,x+2y-z=2 ?
The solution to x+y+z=6,x-y+z=2,x+2y-z=2 is x=1,y=2,z=3