What is x+y+z=6,2x-y+z=3,x-2v+3z=6 ?

The solution to x+y+z=6,2x-y+z=3,x-2v+3z=6 is v=(7z-9)/6 ,x=(-2z-9)/3+6,y=-(z-9)/3

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x+y+z=6,2x-y+z=3,x-2v+3z=6

x + y + z = 6, 2 x - y + z = 3, x - 2 v + 3 z = 6

v = \frac{7 z - 9}{6}, x = \frac{- 2 z - 9}{3} + 6, y = - \frac{z - 9}{3}

Solution steps

x + y + z = 6 2 x - y + z = 3 x - 2 v + 3 z = 6

Isolate

x

for

x + y + z = 6 : x = 6 - y - z

Substitute

x = 6 - y - z

[2 (6 - y - z) - y + z = 3 6 - y - z - 2 v + 3 z = 6]

Simplify

[- 3 y - z + 12 = 3 2 z - y - 2 v + 6 = 6]

Isolate

y

for

- 3 y - z + 12 = 3 : y = - \frac{z - 9}{3}

Substitute

y = - \frac{z - 9}{3}

[2 z - (- \frac{z - 9}{3}) - 2 v + 6 = 6]

Simplify

[- 2 v + \frac{7 z - 9}{3} + 6 = 6]

Isolate

v

for

- 2 v + \frac{7 z - 9}{3} + 6 = 6 : v = \frac{7 z - 9}{6}

Expressing

y

in terms of

z

y = - \frac{z - 9}{3}

For

x = 6 - y - z

Expressing

x

in terms of

z

x = 6 - (- \frac{z - 9}{3}) - z

Simplify

6 - (- \frac{z - 9}{3}) - z : \frac{- 2 z - 9}{3} + 6

x = \frac{- 2 z - 9}{3} + 6

The solutions to the system of equations are:

v = \frac{7 z - 9}{6}, x = \frac{- 2 z - 9}{3} + 6, y = - \frac{z - 9}{3}

2 x + 3 y = 8, x - 4 y = - 7

3 x - 2 y = 14, 2 x - 3 y = 11

x = - 2 + t^{2}, y = 1 - 2 t^{2}

9 p - q = 1, 1 - 3 q - 5 = p

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

What is x+y+z=6,2x-y+z=3,x-2v+3z=6 ?
The solution to x+y+z=6,2x-y+z=3,x-2v+3z=6 is v=(7z-9)/6 ,x=(-2z-9)/3+6,y=-(z-9)/3