What is 2x+y=4,3x+z=6,2y+z=7x+y+z ?

The solution to 2x+y=4,3x+z=6,2y+z=7x+y+z is x= 4/9 ,y= 28/9 ,z= 14/3

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2x+y=4,3x+z=6,2y+z=7x+y+z

2 x + y = 4, 3 x + z = 6, 2 y + z = 7 x + y + z

x = \frac{4}{9}, y = \frac{28}{9}, z = \frac{14}{3}

Solution steps

2 x + y = 4 3 x + z = 6 2 y + z = 7 x + y + z

Isolate

x

for

2 x + y = 4 : x = \frac{4 - y}{2}

Substitute

x = \frac{4 - y}{2}

[3 \cdot \frac{4 - y}{2} + z = 6 2 y + z = 7 \cdot \frac{4 - y}{2} + y + z]

Simplify

[\frac{3 ( 4 - y )}{2} + z = 6 2 y + z = z + \frac{28 - 5 y}{2}]

Isolate

y

for

\frac{3 ( 4 - y )}{2} + z = 6 : y = \frac{2 z}{3}

Substitute

y = \frac{2 z}{3}

[2 \cdot \frac{2 z}{3} + z = z + \frac{28 - 5 \cdot \frac{2 z}{3}}{2}]

Simplify

[\frac{7 z}{3} = \frac{42 - 2 z}{3}]

Isolate

z

for

\frac{7 z}{3} = \frac{42 - 2 z}{3} : z = \frac{14}{3}

For

y = \frac{2 z}{3}

Substitute

z = \frac{14}{3}

y = \frac{2 \cdot \frac{14}{3}}{3}

\frac{2 \cdot \frac{14}{3}}{3} = \frac{28}{9}

y = \frac{28}{9}

For

x = \frac{4 - y}{2}

Substitute

y = \frac{28}{9}, z = \frac{14}{3}

x = \frac{4 - \frac{28}{9}}{2}

\frac{4 - \frac{28}{9}}{2} = \frac{4}{9}

x = \frac{4}{9}

The solutions to the system of equations are:

x = \frac{4}{9}, y = \frac{28}{9}, z = \frac{14}{3}

6 r - 5 t = - 11, 7 t - 8 r = 15

7 x = 5 y + 4, 2 x - 5 y = - 6

2 x + 3 y = 5, 3 x + 4 y = 7

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

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

What is 2x+y=4,3x+z=6,2y+z=7x+y+z ?
The solution to 2x+y=4,3x+z=6,2y+z=7x+y+z is x= 4/9 ,y= 28/9 ,z= 14/3