What is 2x-4y-2z=-14,6x+3y+3z=3,x-5y+8z=13 ?

The solution to 2x-4y-2z=-14,6x+3y+3z=3,x-5y+8z=13 is x=-83/54 ,y= 25/18 ,z= 145/54

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2x-4y-2z=-14,6x+3y+3z=3,x-5y+8z=13

2 x - 4 y - 2 z = - 14, 6 x + 3 y + 3 z = 3, x - 5 y + 8 z = 13

x = - \frac{83}{54}, y = \frac{25}{18}, z = \frac{145}{54}

Solution steps

2 x - 4 y - 2 z = - 14 6 x + 3 y + 3 z = 3 x - 5 y + 8 z = 13

Isolate

x

for

2 x - 4 y - 2 z = - 14 : x = - 7 + 2 y + z

Substitute

x = - 7 + 2 y + z

[6 (- 7 + 2 y + z) + 3 y + 3 z = 3 - 7 + 2 y + z - 5 y + 8 z = 13]

Simplify

[15 y + 9 z - 42 = 3 - 3 y + 9 z - 7 = 13]

Isolate

y

for

15 y + 9 z - 42 = 3 : y = \frac{3 ( - z + 5 )}{5}

Substitute

y = \frac{3 ( - z + 5 )}{5}

[- 3 \cdot \frac{3 ( - z + 5 )}{5} + 9 z - 7 = 13]

Simplify

[\frac{54 z - 45}{5} - 7 = 13]

Isolate

z

for

\frac{54 z - 45}{5} - 7 = 13 : z = \frac{145}{54}

For

y = \frac{3 ( - z + 5 )}{5}

Substitute

z = \frac{145}{54}

y = \frac{3 ( - \frac{145}{54} + 5 )}{5}

\frac{3 ( - \frac{145}{54} + 5 )}{5} = \frac{25}{18}

y = \frac{25}{18}

For

x = - 7 + 2 y + z

Substitute

y = \frac{25}{18}, z = \frac{145}{54}

x = - 7 + 2 \cdot \frac{25}{18} + \frac{145}{54}

- 7 + 2 \cdot \frac{25}{18} + \frac{145}{54} = - \frac{83}{54}

x = - \frac{83}{54}

The solutions to the system of equations are:

x = - \frac{83}{54}, y = \frac{25}{18}, z = \frac{145}{54}

x + y = 7, x + 2 y = 5

m = 3 p - 4, 2 m + p = 12

2 x + 3 y = 8, x + y = 10

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

y = - \frac{1}{2} \cdot x + 2, y = - 2 x + 5

What is 2x-4y-2z=-14,6x+3y+3z=3,x-5y+8z=13 ?
The solution to 2x-4y-2z=-14,6x+3y+3z=3,x-5y+8z=13 is x=-83/54 ,y= 25/18 ,z= 145/54