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

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

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

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

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

Solution steps

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

Isolate

x

for

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

Substitute

x = 6 - y - z

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

Simplify

[- 3 y + 12 = 3 - 2 y - 4 z + 18 = 3]

Isolate

y

for

- 3 y + 12 = 3 : y = 3

Substitute

y = 3

[- 2 \cdot 3 - 4 z + 18 = 3]

Simplify

[- 4 z + 12 = 3]

Isolate

z

for

- 4 z + 12 = 3 : z = \frac{9}{4}

For

x = 6 - y - z

Substitute

y = 3, z = \frac{9}{4}

x = 6 - 3 - \frac{9}{4}

6 - 3 - \frac{9}{4} = \frac{3}{4}

x = \frac{3}{4}

The solutions to the system of equations are:

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

3 x + 4 y = 10, 2 x - 3 y = - 16

x - 1 = 1, x + y = - 1

3 x - 5 y = 5, 4 x + y = - 1

x - 2 y = 4, x + 3 y = 14

x - 2 = 3, x + 63 = 2, x + 59 x = x (x - 1)

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