What is 3x+3y=5,0.62x+3y+2z=8,0.42y+3z=6.5 ?

The solution to 3x+3y=5,0.62x+3y+2z=8,0.42y+3z=6.5 is x=0.41269…,y=1.25396…,z=1.99111…

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3x+3y=5,0.62x+3y+2z=8,0.42y+3z=6.5

3 x + 3 y = 5, 0.62 x + 3 y + 2 z = 8, 0.42 y + 3 z = 6.5

x = 0.41269 \dots, y = 1.25396 \dots, z = 1.99111 \dots

Solution steps

3 x + 3 y = 5 0.62 x + 3 y + 2 z = 8 0.42 y + 3 z = 6.5

Isolate

x

for

3 x + 3 y = 5 : x = \frac{5 - 3 y}{3}

Substitute

x = \frac{5 - 3 y}{3}

[0.42 y + 3 z = 6.5 0.62 \cdot \frac{5 - 3 y}{3} + 3 y + 2 z = 8]

Simplify

[0.42 y + 3 z = 6.5 1.03333 \dots + 2.38 y + 2 z = 8]

Isolate

y

for

0.42 y + 3 z = 6.5 : y = \frac{25 ( - 6 z + 13 )}{21}

Substitute

y = \frac{25 ( - 6 z + 13 )}{21}

[1.03333 \dots + 2.38 \cdot \frac{25 ( - 6 z + 13 )}{21} + 2 z = 8]

Simplify

[- 15 z + 37.86666 \dots = 8]

Isolate

z

for

- 15 z + 37.86666 \dots = 8 : z = 1.99111 \dots

For

y = \frac{25 ( - 6 z + 13 )}{21}

Substitute

z = 1.99111 \dots

y = \frac{25 ( - 6 \cdot 1.99111 \dots + 13 )}{21}

\frac{25 ( - 6 \cdot 1.99111 \dots + 13 )}{21} = 1.25396 \dots

y = 1.25396 \dots

For

x = \frac{5 - 3 y}{3}

Substitute

y = 1.25396 \dots, z = 1.99111 \dots

x = \frac{5 - 3 \cdot 1.25396 \dots}{3}

\frac{5 - 3 \cdot 1.25396 \dots}{3} = 0.41269 \dots

x = 0.41269 \dots

The solutions to the system of equations are:

x = 0.41269 \dots, y = 1.25396 \dots, z = 1.99111 \dots

6 p - 2 q + r = 8, p - q + 4 r = - 15, 4 q - 23 r = 30

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

y - \frac{5}{2} x - 3 y = - 3, x = 2

2 r + 3 s = 1, 4 r - s = 12

2 x + 3 y + 5 = 5, x - 3 y + 9 = 0

What is 3x+3y=5,0.62x+3y+2z=8,0.42y+3z=6.5 ?
The solution to 3x+3y=5,0.62x+3y+2z=8,0.42y+3z=6.5 is x=0.41269…,y=1.25396…,z=1.99111…