What is -y+z=1,x+3y+2z=0,-x-2y-z=0 ?

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

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-y+z=1,x+3y+2z=0,-x-2y-z=0

- y + z = 1, x + 3 y + 2 z = 0, - x - 2 y - z = 0

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

Solution steps

- y + z = 1 x + 3 y + 2 z = 0 - x - 2 y - z = 0

Isolate

y

for

- y + z = 1 : y = - 1 + z

Substitute

y = - 1 + z

[x + 3 (- 1 + z) + 2 z = 0 - x - 2 (- 1 + z) - z = 0]

Simplify

[x - 3 + 5 z = 0 - x + 2 - 3 z = 0]

Isolate

x

for

x - 3 + 5 z = 0 : x = - 5 z + 3

Substitute

x = - 5 z + 3

[- (- 5 z + 3) + 2 - 3 z = 0]

Simplify

[2 z - 1 = 0]

Isolate

z

for

2 z - 1 = 0 : z = \frac{1}{2}

For

x = - 5 z + 3

Substitute

z = \frac{1}{2}

x = - 5 \cdot \frac{1}{2} + 3

- 5 \cdot \frac{1}{2} + 3 = \frac{1}{2}

x = \frac{1}{2}

For

y = - 1 + z

Substitute

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

y = - 1 + \frac{1}{2}

- 1 + \frac{1}{2} = - \frac{1}{2}

y = - \frac{1}{2}

The solutions to the system of equations are:

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

63 x - 5 y = 4, 2 y + 7 = 9 x

4 a + 3 b = 14, 3 a - 4 b = 23

5 x + 2 y = 850, x + 3 y = 300

3 x + y = 8, 6 x + y = 7

5 x - 2 y = 22, 3 x + y = 22

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