What is x-y-2z=0,-2x-6z=1,-x+2y+z=1 ?

The solution to x-y-2z=0,-2x-6z=1,-x+2y+z=1 is x= 1/4 ,y= 3/4 ,z=-1/4

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x-y-2z=0,-2x-6z=1,-x+2y+z=1

x - y - 2 z = 0, - 2 x - 6 z = 1, - x + 2 y + z = 1

x = \frac{1}{4}, y = \frac{3}{4}, z = - \frac{1}{4}

Solution steps

x - y - 2 z = 0 - 2 x - 6 z = 1 - x + 2 y + z = 1

Isolate

x

for

- 2 x - 6 z = 1 : x = - \frac{1 + 6 z}{2}

Substitute

x = - \frac{1 + 6 z}{2}

[- \frac{1 + 6 z}{2} - y - 2 z = 0 - (- \frac{1 + 6 z}{2}) + 2 y + z = 1]

Simplify

[- y + \frac{- 1 - 10 z}{2} = 0 2 y + \frac{1 + 8 z}{2} = 1]

Isolate

y

for

- y + \frac{- 1 - 10 z}{2} = 0 : y = \frac{- 10 z - 1}{2}

Substitute

y = \frac{- 10 z - 1}{2}

[2 \cdot \frac{- 10 z - 1}{2} + \frac{1 + 8 z}{2} = 1]

Simplify

[\frac{1 - 12 z}{2} - 1 = 1]

Isolate

z

for

\frac{1 - 12 z}{2} - 1 = 1 : z = - \frac{1}{4}

For

y = \frac{- 10 z - 1}{2}

Substitute

z = - \frac{1}{4}

y = \frac{- 10 ( - \frac{1}{4} ) - 1}{2}

\frac{- 10 ( - \frac{1}{4} ) - 1}{2} = \frac{3}{4}

y = \frac{3}{4}

For

x = - \frac{1 + 6 z}{2}

Substitute

y = \frac{3}{4}, z = - \frac{1}{4}

x = - \frac{1 + 6 ( - \frac{1}{4} )}{2}

- \frac{1 + 6 ( - \frac{1}{4} )}{2} = \frac{1}{4}

x = \frac{1}{4}

The solutions to the system of equations are:

x = \frac{1}{4}, y = \frac{3}{4}, z = - \frac{1}{4}

12 x + 16 y = 18, 14 x + 18 y = 20

x - y = 6, x + y = - 7

72 x + 3 y = 41, 1 - 4 x - 1 = 18

7.2 m = 1, 5.7 r = 4, 2 n = 50, x = 2

2 x + 2 y = 16, 4 x + 4 y = 32

What is x-y-2z=0,-2x-6z=1,-x+2y+z=1 ?
The solution to x-y-2z=0,-2x-6z=1,-x+2y+z=1 is x= 1/4 ,y= 3/4 ,z=-1/4