What is 31(x+y)+2z=21,3x-(y+z)=6,5x+(x+y-z)=38 ?

The solution to 31(x+y)+2z=21,3x-(y+z)=6,5x+(x+y-z)=38 is x= 862/13 ,y=-1085/13 ,z= 3593/13

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31(x+y)+2z=21,3x-(y+z)=6,5x+(x+y-z)=38

31 (x + y) + 2 z = 21, 3 x - (y + z) = 6, 5 x + (x + y - z) = 38

x = \frac{862}{13}, y = - \frac{1085}{13}, z = \frac{3593}{13}

Solution steps

31 (x + y) + 2 z = 21 3 x - (y + z) = 6 5 x + (x + y - z) = 38

Isolate

x

for

31 (x + y) + 2 z = 21 : x = \frac{21 - 2 z}{31} - y

Substitute

x = \frac{21 - 2 z}{31} - y

[3 (\frac{21 - 2 z}{31} - y) - (y + z) = 6 5 (\frac{21 - 2 z}{31} - y) + \frac{21 - 2 z}{31} - y + y - z = 38]

Simplify

[- 4 y + \frac{63 - 37 z}{31} = 6 \frac{- 43 z + 126}{31} - 5 y = 38]

Isolate

y

for

- 4 y + \frac{63 - 37 z}{31} = 6 : y = - \frac{37 z + 123}{124}

Substitute

y = - \frac{37 z + 123}{124}

[\frac{- 43 z + 126}{31} - 5 (- \frac{37 z + 123}{124}) = 38]

Simplify

[\frac{13 z + 1119}{124} = 38]

Isolate

z

for

\frac{13 z + 1119}{124} = 38 : z = \frac{3593}{13}

For

y = - \frac{37 z + 123}{124}

Substitute

z = \frac{3593}{13}

y = - \frac{37 \cdot \frac{3593}{13} + 123}{124}

- \frac{37 \cdot \frac{3593}{13} + 123}{124} = - \frac{1085}{13}

y = - \frac{1085}{13}

For

x = \frac{21 - 2 z}{31} - y

Substitute

y = - \frac{1085}{13}, z = \frac{3593}{13}

x = \frac{21 - 2 \cdot \frac{3593}{13}}{31} - (- \frac{1085}{13})

\frac{21 - 2 \cdot \frac{3593}{13}}{31} - (- \frac{1085}{13}) = \frac{862}{13}

x = \frac{862}{13}

The solutions to the system of equations are:

x = \frac{862}{13}, y = - \frac{1085}{13}, z = \frac{3593}{13}

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

5 x + 2 y = 24, 4 x + 3 y = 29

y = 2 x - 1, 2 y - x = 7

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

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

What is 31(x+y)+2z=21,3x-(y+z)=6,5x+(x+y-z)=38 ?
The solution to 31(x+y)+2z=21,3x-(y+z)=6,5x+(x+y-z)=38 is x= 862/13 ,y=-1085/13 ,z= 3593/13