What is 2x+3y+2z=7,0.83x+2y=5,0.22y+3z=6.1 ?

The solution to 2x+3y+2z=7,0.83x+2y=5,0.22y+3z=6.1 is x=-5.14789…,y=4.63637…,z= 20723/12238

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2x+3y+2z=7,0.83x+2y=5,0.22y+3z=6.1

2 x + 3 y + 2 z = 7, 0.83 x + 2 y = 5, 0.22 y + 3 z = 6.1

x = - 5.14789 \dots, y = 4.63637 \dots, z = \frac{20723}{12238}

Solution steps

2 x + 3 y + 2 z = 7 0.83 x + 2 y = 5 0.22 y + 3 z = 6.1

Isolate

x

for

0.83 x + 2 y = 5 : x = \frac{500 - 200 y}{83}

Substitute

x = \frac{500 - 200 y}{83}

[0.22 y + 3 z = 6.1 2 \cdot \frac{500 - 200 y}{83} + 3 y + 2 z = 7]

Simplify

[0.22 y + 3 z = 6.1 2 z + \frac{1000 - 151 y}{83} = 7]

Isolate

y

for

0.22 y + 3 z = 6.1 : y = \frac{5 ( - 30 z + 61 )}{11}

Substitute

y = \frac{5 ( - 30 z + 61 )}{11}

[2 z + \frac{1000 - 151 \cdot \frac{5 ( - 30 z + 61 )}{11}}{83} = 7]

Simplify

[\frac{24476 z - 35055}{913} = 7]

Isolate

z

for

\frac{24476 z - 35055}{913} = 7 : z = \frac{20723}{12238}

For

y = \frac{5 ( - 30 z + 61 )}{11}

Substitute

z = \frac{20723}{12238}

y = \frac{5 ( - 30 \cdot \frac{20723}{12238} + 61 )}{11}

\frac{5 ( - 30 \cdot \frac{20723}{12238} + 61 )}{11} = 4.63637 \dots

y = 4.63637 \dots

For

x = \frac{500 - 200 y}{83}

Substitute

y = 4.63637 \dots, z = \frac{20723}{12238}

x = \frac{500 - 200 \cdot 4.63637 \dots}{83}

\frac{500 - 200 \cdot 4.63637 \dots}{83} = - 5.14789 \dots

x = - 5.14789 \dots

The solutions to the system of equations are:

x = - 5.14789 \dots, y = 4.63637 \dots, z = \frac{20723}{12238}

2 \cdot 2 x - 3 \cdot 1 + 3 \cdot 2 = 0, 0.4 x + y - 88 = 0

x - 2 y = 17, 7 x - 6 y = 47

2 x + 7 y = 17, 5 x + 3 y = - 1

x + y = 2, x - y = 20

5 x + 3 y = - 7, 3 x - 2 y = - 8

What is 2x+3y+2z=7,0.83x+2y=5,0.22y+3z=6.1 ?
The solution to 2x+3y+2z=7,0.83x+2y=5,0.22y+3z=6.1 is x=-5.14789…,y=4.63637…,z= 20723/12238