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

The solution to x+y-z=1,x-y+z=2,-x+y+z=3 is x= 3/2 ,y=2,z= 5/2

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

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

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

Solution steps

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

Isolate

x

for

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

Substitute

x = 1 - y + z

[1 - y + z - y + z = 2 - (1 - y + z) + y + z = 3]

Simplify

[- 2 y + 2 z + 1 = 2 2 y - 1 = 3]

Isolate

y

for

2 y - 1 = 3 : y = 2

Substitute

y = 2

[- 2 \cdot 2 + 2 z + 1 = 2]

Simplify

[2 z - 3 = 2]

Isolate

z

for

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

For

x = 1 - y + z

Substitute

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

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

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

x = \frac{3}{2}

The solutions to the system of equations are:

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

2 x + y = 7, x - 3 y = 16

3 x + 4 y = 17, 2 x - 5 y = 19

x - y = 9, 2 x + 3 y = 6

(r) \cdot 5 x + 2 y - 5 = 0, e (s) \cdot 2 x - 5 y + 9 = 0

24 x + 21 y = 12, 24 x - 12 y = 24

What is x+y-z=1,x-y+z=2,-x+y+z=3 ?
The solution to x+y-z=1,x-y+z=2,-x+y+z=3 is x= 3/2 ,y=2,z= 5/2