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

The solution to 2x+y+z=0,4x+3y+2z=2,2x-y-3z=0 is x=-1/2 ,y=2,z=-1

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

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

x = - \frac{1}{2}, y = 2, z = - 1

Solution steps

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

Isolate

x

for

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

Substitute

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

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

Simplify

[y = 2 - 2 y - 4 z = 0]

Substitute

y = 2

[- 2 \cdot 2 - 4 z = 0]

Simplify

[- 4 - 4 z = 0]

Isolate

z

for

- 4 - 4 z = 0 : z = - 1

For

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

Substitute

y = 2, z = - 1

x = \frac{- 2 - ( - 1 )}{2}

\frac{- 2 - ( - 1 )}{2} = - \frac{1}{2}

x = - \frac{1}{2}

The solutions to the system of equations are:

x = - \frac{1}{2}, y = 2, z = - 1

2 x + 3 y = 8, 5 x - 2 y = 1

2 a + 3 y (a) = 4, 3 a + y (a) = 5

x + y = 6, 2 x + y = 20

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

y - 4 = 1, 6 x - 5 y = 9

What is 2x+y+z=0,4x+3y+2z=2,2x-y-3z=0 ?
The solution to 2x+y+z=0,4x+3y+2z=2,2x-y-3z=0 is x=-1/2 ,y=2,z=-1