GMAT Simultaneous Equations Explained — X+y=2 and x^{2}+y^{2}=2, what is the value of x y ?

If x + y = 2 and x^{2} + y^{2} = 2, what is the value of x y ?

simultaneous equationsdevelopment formulas

Explanation	Calculations	Help
$We apply the development formula for the square of a sum.$	$(x + y)^{2} = x^{2} + y^{2} + 2 x y$	Theory & Tactics Method Card EXP4-A Click to view full details
$We substitute the known values (x + y)^{2} = 2^{2} = 4 and x^{2} + y^{2} = 2 into the expansion.$	$4 = 2 + 2 x y$	Theory & Tactics Method Card EQUA3-A Click to view full details
$We isolate the term x y by subtracting 2 from both sides.$	$4 - 2 = 2 x y$	Theory & Tactics Method Card EQUA1-B Click to view full details
$We solve for x y by dividing both sides by 2.$	$\frac{4 - 2}{2} = x y$	Theory & Tactics Method Card EQUA1-C Click to view full details

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