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Re: x/w- x/y=0 and w^2 + 4 = 4w [#permalink]
1
First Equation:

frac{x}{w} - frac{x}{y} = 0


Multiplying both sides by ( w cdot y ) to clear the denominators:

x cdot y - x cdot w = 0


Factoring out the common term of ( x ):

x(y - w) = 0


This gives us two cases:
1. ( x = 0 )
2. ( y = w )

Second Equation:

w^2 + 4 = 4w


Moving terms to one side:

w^2 - 4w + 4 = 0


Factoring:

(w - 2)^2 = 0


So, the only solution for ( w ) is ( w = 2 ).

[b]Solutions:[b]
1. If ( x = 0), the first equation holds for any ( w ) and ( y ).
2. If ( y = w = 2), the first equation also holds.

Therefore, the solutions to the system are:
- ( x = 0 ) (with any ( w ) and ( y ))
- ( y = 2 ) and ( w = 2 ) (with ( x ) being any value)
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