What is 2x+y-2z=1,x-2y+3z=6,3x-3y-z=5 ?

The solution to 2x+y-2z=1,x-2y+3z=6,3x-3y-z=5 is x= 24/13 ,y=-3/13 ,z= 16/13

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2x+y-2z=1,x-2y+3z=6,3x-3y-z=5

2 x + y - 2 z = 1, x - 2 y + 3 z = 6, 3 x - 3 y - z = 5

x = \frac{24}{13}, y = - \frac{3}{13}, z = \frac{16}{13}

Solution steps

2 x + y - 2 z = 1 x - 2 y + 3 z = 6 3 x - 3 y - z = 5

Isolate

x

for

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

Substitute

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

[\frac{1 - y + 2 z}{2} - 2 y + 3 z = 6 3 \cdot \frac{1 - y + 2 z}{2} - 3 y - z = 5]

Simplify

[\frac{- 5 y + 8 z + 1}{2} = 6 \frac{- 9 y + 4 z + 3}{2} = 5]

Isolate

y

for

\frac{- 5 y + 8 z + 1}{2} = 6 : y = - \frac{- 8 z + 11}{5}

Substitute

y = - \frac{- 8 z + 11}{5}

[\frac{- 9 ( - \frac{- 8 z + 11}{5} ) + 4 z + 3}{2} = 5]

Simplify

[\frac{- 26 z + 57}{5} = 5]

Isolate

z

for

\frac{- 26 z + 57}{5} = 5 : z = \frac{16}{13}

For

y = - \frac{- 8 z + 11}{5}

Substitute

z = \frac{16}{13}

y = - \frac{- 8 \cdot \frac{16}{13} + 11}{5}

- \frac{- 8 \cdot \frac{16}{13} + 11}{5} = - \frac{3}{13}

y = - \frac{3}{13}

For

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

Substitute

y = - \frac{3}{13}, z = \frac{16}{13}

x = \frac{1 - ( - \frac{3}{13} ) + 2 \cdot \frac{16}{13}}{2}

\frac{1 - ( - \frac{3}{13} ) + 2 \cdot \frac{16}{13}}{2} = \frac{24}{13}

x = \frac{24}{13}

The solutions to the system of equations are:

x = \frac{24}{13}, y = - \frac{3}{13}, z = \frac{16}{13}

x + \frac{y}{4} = - 1, x + y = 1

2 x + 3 y + 4 z = 3, 2 x + 6 y + 8 z = 5, 4 x + 9 y - 4 z = 4

x + 3 y = 3, 2 x - y = 1.8

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

x + 3 y = 1, 2 - 2 x - 4 y = 24

What is 2x+y-2z=1,x-2y+3z=6,3x-3y-z=5 ?
The solution to 2x+y-2z=1,x-2y+3z=6,3x-3y-z=5 is x= 24/13 ,y=-3/13 ,z= 16/13