What is x+y+z=1,3x-y+2z=7,3x+y-z=23 ?

The solution to x+y+z=1,3x-y+2z=7,3x+y-z=23 is x= 41/7 ,y= 2/7 ,z=-36/7

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x+y+z=1,3x-y+2z=7,3x+y-z=23

x + y + z = 1, 3 x - y + 2 z = 7, 3 x + y - z = 23

x = \frac{41}{7}, y = \frac{2}{7}, z = - \frac{36}{7}

Solution steps

x + y + z = 1 3 x - y + 2 z = 7 3 x + y - z = 23

Isolate

x

for

x + y + z = 1 : x = 1 - y - z

Substitute

x = 1 - y - z

[3 (1 - y - z) - y + 2 z = 7 3 (1 - y - z) + y - z = 23]

Simplify

[- 4 y - z + 3 = 7 - 2 y - 4 z + 3 = 23]

Isolate

y

for

- 4 y - z + 3 = 7 : y = - \frac{z + 4}{4}

Substitute

y = - \frac{z + 4}{4}

[- 2 (- \frac{z + 4}{4}) - 4 z + 3 = 23]

Simplify

[\frac{- 7 z + 4}{2} + 3 = 23]

Isolate

z

for

\frac{- 7 z + 4}{2} + 3 = 23 : z = - \frac{36}{7}

For

y = - \frac{z + 4}{4}

Substitute

z = - \frac{36}{7}

y = - \frac{- \frac{36}{7} + 4}{4}

- \frac{- \frac{36}{7} + 4}{4} = \frac{2}{7}

y = \frac{2}{7}

For

x = 1 - y - z

Substitute

y = \frac{2}{7}, z = - \frac{36}{7}

x = 1 - \frac{2}{7} - (- \frac{36}{7})

1 - \frac{2}{7} - (- \frac{36}{7}) = \frac{41}{7}

x = \frac{41}{7}

The solutions to the system of equations are:

x = \frac{41}{7}, y = \frac{2}{7}, z = - \frac{36}{7}

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

5 x + 2 y = 23, 3 x + 3 y = 21

5 x + 8 y = 1, 7 - 4 x + 7 y = 16

47 x + 53 y = 147, 53 x + 47 y = 53

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

What is x+y+z=1,3x-y+2z=7,3x+y-z=23 ?
The solution to x+y+z=1,3x-y+2z=7,3x+y-z=23 is x= 41/7 ,y= 2/7 ,z=-36/7