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(1) \(xy = x\). Re-arrange and factor out \(x\) to get \(x(y-1)=0\). So, either \(x=0\) (and \(y\) can take any value) OR \(y=1\) (and \(x\) can take any value). Not sufficient.
(2) \(x+y=x\). This statemnt implies that \(y=0\). Not sufficient to answer whether \(x=0\).
(1)+(2) As from (2) \(y=0\neq{1}\) then according to (1) \(x=0\). Sufficient.
I think this is a high-quality question and I agree with explanation. I'm confused as to why I cannot divide statement 1 by zero to get to y=1. I know that x=0 is clearly a possibility i just don't get why I cannot divide both sides by X.
I think this is a high-quality question and I agree with explanation. I'm confused as to why I cannot divide statement 1 by zero to get to y=1. I know that x=0 is clearly a possibility i just don't get why I cannot divide both sides by X.
If you divide (reduce) xy = x by x, you assume, with no ground for it, that x does not equal to zero thus exclude a possible solution.
Never reduce equation by variable (or expression with variable), if you are not certain that variable (or expression with variable) doesn't equal to zero. We cannot divide by zero. _________________
why we cannot have a situation where both x and y are zero??it satisfies both the equations..and it has not been explicitly mentioned x and y are different??
why we cannot have a situation where both x and y are zero??it satisfies both the equations..and it has not been explicitly mentioned x and y are different??
But we have precisely the situation you describe: when we combine the statements we get that x = y = 0.
_________________
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58% (00:48) correct 
