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If xy+z = x(y+z), which of the following must be true? 1, [#permalink]
09 Dec 2007, 19:08
If xy+z = x(y+z), which of the following must be true?
1, x=0 and z=0
2, x=1 and y=1
3, y=1 and z=0
4, x=1 or y=0
5, x=1 or z=0
The correct answer is Choice 5. I selected the right answer through process of elimination but would like to know the best way to get the answer correctly. The way I tried to simplify the equation is defined below, please let me know what I am doing wrong.
xy+z = x(y+z), so
xy+z = xy +xz
z = xy-xy+xz (both xy cancel out)
z = xz (divide both by side by z)
z/z = x
The solution above does not provide answer to value of z or y. What is the best way to solve this equation? Thanks in advance for your explanation.