What is 3x+2y+z=2,4x+2y+2z=8,x-y+z=4 ?

The solution to 3x+2y+z=2,4x+2y+2z=8,x-y+z=4 is x=-4,y=2,z=10

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3x+2y+z=2,4x+2y+2z=8,x-y+z=4

3 x + 2 y + z = 2, 4 x + 2 y + 2 z = 8, x - y + z = 4

x = - 4, y = 2, z = 10

Solution steps

3 x + 2 y + z = 2 4 x + 2 y + 2 z = 8 x - y + z = 4

Isolate

x

for

3 x + 2 y + z = 2 : x = \frac{2 - 2 y - z}{3}

Substitute

x = \frac{2 - 2 y - z}{3}

[4 \cdot \frac{2 - 2 y - z}{3} + 2 y + 2 z = 8 \frac{2 - 2 y - z}{3} - y + z = 4]

Simplify

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

Isolate

y

for

\frac{- 2 y + 2 z + 8}{3} = 8 : y = z - 8

Substitute

y = z - 8

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

Simplify

[- z + 14 = 4]

Isolate

z

for

- z + 14 = 4 : z = 10

For

y = z - 8

Substitute

z = 10

y = 10 - 8

Simplify

y = 2

For

x = \frac{2 - 2 y - z}{3}

Substitute

y = 2, z = 10

x = \frac{2 - 2 \cdot 2 - 10}{3}

\frac{2 - 2 \cdot 2 - 10}{3} = - 4

x = - 4

The solutions to the system of equations are:

x = - 4, y = 2, z = 10

- 4 x + 6 y = 21, 5 x - 6 y = 9

x - y = - 1, 2 x - y = 1

0.19 + 0.18 + 3.27 y = 6, x = 0

5 x + 3 y = 71, 7 x - y = 7

2 x + 3 y = - 13, - 5 x - 2 y = 16

What is 3x+2y+z=2,4x+2y+2z=8,x-y+z=4 ?
The solution to 3x+2y+z=2,4x+2y+2z=8,x-y+z=4 is x=-4,y=2,z=10