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116.5685 and 3.4315 (accurate to 4 decimal places)
1. x * y = 400
2. x + y = 120
Rearranging 2 gives
3. y = -x + 120
Substituting this value for y into 1. gives
x * (-x + 120) = 400
-x2 + 120x = 400
-x2 + 120x - 400 = 0
This is now a quadratic equation and can be solved using the quadratic formula.
x = (-120 +/- (1202 - 4*-1*-400)1/2) / (2 * -1)
x = 116.5685 and 3.4315 (to 4 decimal places)
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