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

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

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

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

x = \frac{- z - 1}{3} + 2, y = - \frac{- 4 z - 1}{3}

Solution steps

[x + y - z = 2 2 x - y + 2 z = 3]

Isolate

x

for

x + y - z = 2 : x = 2 - y + z

Substitute

x = 2 - y + z

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

Simplify

[- 3 y + 4 z + 4 = 3]

Isolate

y

for

- 3 y + 4 z + 4 = 3 : y = - \frac{- 4 z - 1}{3}

For

x = 2 - y + z

Expressing

x

in terms of

z

x = 2 - (- \frac{- 4 z - 1}{3}) + z

Simplify

2 - (- \frac{- 4 z - 1}{3}) + z : \frac{- z - 1}{3} + 2

x = \frac{- z - 1}{3} + 2

The solutions to the system of equations are:

x = \frac{- z - 1}{3} + 2, y = - \frac{- 4 z - 1}{3}

3 x + 2 y = 1, 1 x - 4 y = 13

2 x + y = 1, - x + 2 y = 9

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

x + 2 y = 9, 3 x - 2 y = - 5

x + y = 6, x = 1 y - 2

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