What is 2+3y+4z=7,4y=2+5z,3z-2x+6=0 ?

The solution to 2+3y+4z=7,4y=2+5z,3z-2x+6=0 is x= 114/31 ,y= 33/31 ,z= 14/31

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2+3y+4z=7,4y=2+5z,3z-2x+6=0

2 + 3 y + 4 z = 7, 4 y = 2 + 5 z, 3 z - 2 x + 6 = 0

x = \frac{114}{31}, y = \frac{33}{31}, z = \frac{14}{31}

Solution steps

2 + 3 y + 4 z = 7 4 y = 2 + 5 z 3 z - 2 x + 6 = 0

Isolate

y

for

2 + 3 y + 4 z = 7 : y = \frac{- 4 z + 5}{3}

Substitute

y = \frac{- 4 z + 5}{3}

[4 \cdot \frac{- 4 z + 5}{3} = 2 + 5 z 3 z - 2 x + 6 = 0]

Simplify

[\frac{4 ( - 4 z + 5 )}{3} = 2 + 5 z 3 z - 2 x + 6 = 0]

Isolate

z

for

\frac{4 ( - 4 z + 5 )}{3} = 2 + 5 z : z = \frac{14}{31}

Substitute

z = \frac{14}{31}

[3 \cdot \frac{14}{31} - 2 x + 6 = 0]

Simplify

[- 2 x + \frac{228}{31} = 0]

Isolate

x

for

- 2 x + \frac{228}{31} = 0 : x = \frac{114}{31}

For

y = \frac{- 4 z + 5}{3}

Substitute

x = \frac{114}{31}, z = \frac{14}{31}

y = \frac{- 4 \cdot \frac{14}{31} + 5}{3}

\frac{- 4 \cdot \frac{14}{31} + 5}{3} = \frac{33}{31}

y = \frac{33}{31}

The solutions to the system of equations are:

x = \frac{114}{31}, y = \frac{33}{31}, z = \frac{14}{31}

2 x + 3 y = 5, 3 x + 2 y = 7, 3 x - 2 y = 1

2 x + 3 y - z = 18, x - 2 y + 4 z = 21, 3 x - y - 3 z = 3

2 x + 4 y = 7, 3 x - 6 y = 10

2 x + 4 y = 16, 4 x + 3 y = 24

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

What is 2+3y+4z=7,4y=2+5z,3z-2x+6=0 ?
The solution to 2+3y+4z=7,4y=2+5z,3z-2x+6=0 is x= 114/31 ,y= 33/31 ,z= 14/31