What is x+y=2,x-z=0,w(x,y,z)=2x+y-z ?

The solution to x+y=2,x-z=0,w(x,y,z)=2x+y-z is x=z,y=-z+2,w=2

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x+y=2,x-z=0,w(x,y,z)=2x+y-z

x + y = 2, x - z = 0, w (x, y, z) = 2 x + y - z

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

Solution steps

x + y = 2 x - z = 0 w = 2 x + y - z

[x + y = 2 x - z = 0]

Isolate

x

for

x + y = 2 : x = 2 - y

Substitute

x = 2 - y

[2 - y - z = 0]

Isolate

y

for

2 - y - z = 0 : y = - z + 2

For

x = 2 - y

Expressing

x

in terms of

z

x = 2 - (- z + 2)

Simplify

2 - (- z + 2) : z

x = z

For

w = 2 x + y - z

Expressing

w

in terms of

z

w = 2 z - z + 2 - z

2 z - z + 2 - z = 2

w = 2

The solutions to the system of equations are:

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

\frac{2}{x} - \frac{3}{y} = 9, \frac{5}{x} + \frac{1}{y} = 7

y = 2 x + 9, 3 x + 2 y = 4

4 x - y = - 12, 4 x + 2 y = 0

31 (x + y) + 2 z = 21, 3 x - (y + z) = 6, 5 x + (x + y - z) = 38

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

What is x+y=2,x-z=0,w(x,y,z)=2x+y-z ?
The solution to x+y=2,x-z=0,w(x,y,z)=2x+y-z is x=z,y=-z+2,w=2