What is 4x-y+5z=-6,3x+3y-4z=30,6x+2y-3z=33 ?

The solution to 4x-y+5z=-6,3x+3y-4z=30,6x+2y-3z=33 is x=3,y=3,z=-3

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4x-y+5z=-6,3x+3y-4z=30,6x+2y-3z=33

4 x - y + 5 z = - 6, 3 x + 3 y - 4 z = 30, 6 x + 2 y - 3 z = 33

x = 3, y = 3, z = - 3

Solution steps

4 x - y + 5 z = - 6 3 x + 3 y - 4 z = 30 6 x + 2 y - 3 z = 33

Isolate

x

for

4 x - y + 5 z = - 6 : x = \frac{- 6 + y - 5 z}{4}

Substitute

x = \frac{- 6 + y - 5 z}{4}

[3 \cdot \frac{- 6 + y - 5 z}{4} + 3 y - 4 z = 30 6 \cdot \frac{- 6 + y - 5 z}{4} + 2 y - 3 z = 33]

Simplify

[\frac{15 y - 31 z - 18}{4} = 30 \frac{7 y - 21 z - 18}{2} = 33]

Isolate

y

for

\frac{15 y - 31 z - 18}{4} = 30 : y = \frac{31 z + 138}{15}

Substitute

y = \frac{31 z + 138}{15}

[\frac{7 \cdot \frac{31 z + 138}{15} - 21 z - 18}{2} = 33]

Simplify

[\frac{- 49 z + 348}{15} = 33]

Isolate

z

for

\frac{- 49 z + 348}{15} = 33 : z = - 3

For

y = \frac{31 z + 138}{15}

Substitute

z = - 3

y = \frac{31 ( - 3 ) + 138}{15}

\frac{31 ( - 3 ) + 138}{15} = 3

y = 3

For

x = \frac{- 6 + y - 5 z}{4}

Substitute

y = 3, z = - 3

x = \frac{- 6 + 3 - 5 ( - 3 )}{4}

\frac{- 6 + 3 - 5 ( - 3 )}{4} = 3

x = 3

The solutions to the system of equations are:

x = 3, y = 3, z = - 3

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

3 x = 3, 46 = x + 108

- 6 x + 3 y = 1, 8 - 5 x - 2 y = - 3

3 x + 6 y = 39, 0 x + 3 y = 1300

(a) x + 2 y + 3 z = 4, - x + 4 y - 5 z = - 2 x, 2 x - 3 y + 4 z = 27

What is 4x-y+5z=-6,3x+3y-4z=30,6x+2y-3z=33 ?
The solution to 4x-y+5z=-6,3x+3y-4z=30,6x+2y-3z=33 is x=3,y=3,z=-3