What is x+y-2z=8,2x-y+z=3,3x+y+2z=6 ?

The solution to x+y-2z=8,2x-y+z=3,3x+y+2z=6 is x=3,y=1,z=-2

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x+y-2z=8,2x-y+z=3,3x+y+2z=6

x + y - 2 z = 8, 2 x - y + z = 3, 3 x + y + 2 z = 6

x = 3, y = 1, z = - 2

Solution steps

x + y - 2 z = 8 2 x - y + z = 3 3 x + y + 2 z = 6

Isolate

x

for

x + y - 2 z = 8 : x = 8 - y + 2 z

Substitute

x = 8 - y + 2 z

[2 (8 - y + 2 z) - y + z = 3 3 (8 - y + 2 z) + y + 2 z = 6]

Simplify

[- 3 y + 5 z + 16 = 3 - 2 y + 8 z + 24 = 6]

Isolate

y

for

- 3 y + 5 z + 16 = 3 : y = - \frac{- 5 z - 13}{3}

Substitute

y = - \frac{- 5 z - 13}{3}

[- 2 (- \frac{- 5 z - 13}{3}) + 8 z + 24 = 6]

Simplify

[\frac{14 z - 26}{3} + 24 = 6]

Isolate

z

for

\frac{14 z - 26}{3} + 24 = 6 : z = - 2

For

y = - \frac{- 5 z - 13}{3}

Substitute

z = - 2

y = - \frac{- 5 ( - 2 ) - 13}{3}

- \frac{- 5 ( - 2 ) - 13}{3} = 1

y = 1

For

x = 8 - y + 2 z

Substitute

y = 1, z = - 2

x = 8 - 1 + 2 (- 2)

8 - 1 + 2 (- 2) = 3

x = 3

The solutions to the system of equations are:

x = 3, y = 1, z = - 2

- m + n = - 1, 4 m - 2 n = 5

4 (x - y) = - 2, 3 x - 7 y = - 25 - 2 (x + y)

x - y = 3, 2 x + 4 y = 12

x + y = 2, 4 - 3 x + y = 0

2 x - 3 y = 8, 4 x - 6 y = 9

What is x+y-2z=8,2x-y+z=3,3x+y+2z=6 ?
The solution to x+y-2z=8,2x-y+z=3,3x+y+2z=6 is x=3,y=1,z=-2