What is 2x+y-3z=0,4x+2y-6z=0,x-y+z=0 ?

The solution to 2x+y-3z=0,4x+2y-6z=0,x-y+z=0 is x=(2z)/3 ,y=(5z)/3

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2x+y-3z=0,4x+2y-6z=0,x-y+z=0

2 x + y - 3 z = 0, 4 x + 2 y - 6 z = 0, x - y + z = 0

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

Solution steps

2 x + y - 3 z = 0 4 x + 2 y - 6 z = 0 x - y + z = 0

Isolate

x

for

2 x + y - 3 z = 0 : x = \frac{- y + 3 z}{2}

Substitute

x = \frac{- y + 3 z}{2}

[4 \cdot \frac{- y + 3 z}{2} + 2 y - 6 z = 0 \frac{- y + 3 z}{2} - y + z = 0]

Simplify

[0 = 0 \frac{- 3 y + 5 z}{2} = 0]

Isolate

y

for

\frac{- 3 y + 5 z}{2} = 0 : y = \frac{5 z}{3}

For

x = \frac{- y + 3 z}{2}

Expressing

x

in terms of

z

x = \frac{- \frac{5 z}{3} + 3 z}{2}

Simplify

\frac{- \frac{5 z}{3} + 3 z}{2} : \frac{2 z}{3}

x = \frac{2 z}{3}

The solutions to the system of equations are:

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

2 x + 3 y = 13, 4 x - y = - 2

7 x - 3 y = 10, 3 x - 5 y = - 5

2 x + y = 10, x + y = 7

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

3 q + 2 q = 21, 7 p + 4 q = 47

What is 2x+y-3z=0,4x+2y-6z=0,x-y+z=0 ?
The solution to 2x+y-3z=0,4x+2y-6z=0,x-y+z=0 is x=(2z)/3 ,y=(5z)/3