What is 3x+2y+6z=24,2x+4y+3z=23,5x+3y+4z=33 ?

The solution to 3x+2y+6z=24,2x+4y+3z=23,5x+3y+4z=33 is x=4,y=3,z=1

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3x+2y+6z=24,2x+4y+3z=23,5x+3y+4z=33

3 x + 2 y + 6 z = 24, 2 x + 4 y + 3 z = 23, 5 x + 3 y + 4 z = 33

x = 4, y = 3, z = 1

Solution steps

3 x + 2 y + 6 z = 24 2 x + 4 y + 3 z = 23 5 x + 3 y + 4 z = 33

Isolate

x

for

3 x + 2 y + 6 z = 24 : x = \frac{24 - 2 y - 6 z}{3}

Substitute

x = \frac{24 - 2 y - 6 z}{3}

[2 \cdot \frac{24 - 2 y - 6 z}{3} + 4 y + 3 z = 23 5 \cdot \frac{24 - 2 y - 6 z}{3} + 3 y + 4 z = 33]

Simplify

[\frac{8 y - 3 z + 48}{3} = 23 \frac{- y - 18 z + 120}{3} = 33]

Isolate

y

for

\frac{8 y - 3 z + 48}{3} = 23 : y = \frac{3 z + 21}{8}

Substitute

y = \frac{3 z + 21}{8}

[\frac{- \frac{3 z + 21}{8} - 18 z + 120}{3} = 33]

Simplify

[\frac{- 49 z + 313}{8} = 33]

Isolate

z

for

\frac{- 49 z + 313}{8} = 33 : z = 1

For

y = \frac{3 z + 21}{8}

Substitute

z = 1

y = \frac{3 \cdot 1 + 21}{8}

\frac{3 \cdot 1 + 21}{8} = 3

y = 3

For

x = \frac{24 - 2 y - 6 z}{3}

Substitute

y = 3, z = 1

x = \frac{24 - 2 \cdot 3 - 6 \cdot 1}{3}

\frac{24 - 2 \cdot 3 - 6 \cdot 1}{3} = 4

x = 4

The solutions to the system of equations are:

x = 4, y = 3, z = 1

x + 6 y = 7, 2 x + y = 3

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

3 x + y = 4, - 6 x - 2 y = 1

7 x + 4 y = 13, 5 x - 2 y = 19

x + y = 4, x + 2 y = 6

What is 3x+2y+6z=24,2x+4y+3z=23,5x+3y+4z=33 ?
The solution to 3x+2y+6z=24,2x+4y+3z=23,5x+3y+4z=33 is x=4,y=3,z=1