What is 3x+y+z=1,x+2y-z=1,x+y+2z=17 ?

The solution to 3x+y+z=1,x+2y-z=1,x+y+2z=17 is x=-47/11 ,y= 70/11 ,z= 82/11

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3x+y+z=1,x+2y-z=1,x+y+2z=17

3 x + y + z = 1, x + 2 y - z = 1, x + y + 2 z = 17

x = - \frac{47}{11}, y = \frac{70}{11}, z = \frac{82}{11}

Solution steps

3 x + y + z = 1 x + 2 y - z = 1 x + y + 2 z = 17

Isolate

x

for

3 x + y + z = 1 : x = \frac{1 - y - z}{3}

Substitute

x = \frac{1 - y - z}{3}

[\frac{1 - y - z}{3} + 2 y - z = 1 \frac{1 - y - z}{3} + y + 2 z = 17]

Simplify

[\frac{5 y - 4 z + 1}{3} = 1 \frac{2 y + 5 z + 1}{3} = 17]

Isolate

y

for

\frac{5 y - 4 z + 1}{3} = 1 : y = \frac{4 z + 2}{5}

Substitute

y = \frac{4 z + 2}{5}

[\frac{2 \cdot \frac{4 z + 2}{5} + 5 z + 1}{3} = 17]

Simplify

[\frac{11 z + 3}{5} = 17]

Isolate

z

for

\frac{11 z + 3}{5} = 17 : z = \frac{82}{11}

For

y = \frac{4 z + 2}{5}

Substitute

z = \frac{82}{11}

y = \frac{4 \cdot \frac{82}{11} + 2}{5}

\frac{4 \cdot \frac{82}{11} + 2}{5} = \frac{70}{11}

y = \frac{70}{11}

For

x = \frac{1 - y - z}{3}

Substitute

y = \frac{70}{11}, z = \frac{82}{11}

x = \frac{1 - \frac{70}{11} - \frac{82}{11}}{3}

\frac{1 - \frac{70}{11} - \frac{82}{11}}{3} = - \frac{47}{11}

x = - \frac{47}{11}

The solutions to the system of equations are:

x = - \frac{47}{11}, y = \frac{70}{11}, z = \frac{82}{11}

4 x + y = 1, 4 x - 2 y = 10

y = \frac{4}{5} x + 8, 2 x + y = - 6

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

2 x + 3 y + b = 0, 4 x = 3 y

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

What is 3x+y+z=1,x+2y-z=1,x+y+2z=17 ?
The solution to 3x+y+z=1,x+2y-z=1,x+y+2z=17 is x=-47/11 ,y= 70/11 ,z= 82/11