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99x + 101y = 499; 101x + 99y = 501

99x + 101y = 499; 101x + 99y = 501

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99x + 101y = 499 ... (I) 101x + 99y = 501 ... (II) By adding the both equations 99x + 101y = 499 +101x + 99y = 501 _____________________ 200x + 200y = 1000 Dividing both sides of the equation by 200 X + y = 5 ... (III) Let's subtract equation (II) from (I) 99x + 101y = 499 -101x + 99y = 501 ___________________ -2x + 2y = -2 Dividing both sides of the equation by 2 -x + y = -1 ... (IV) Adding equations (III) and (IV) x + y = 5 +x + y = -1 ___________ 2y = 4 ? y = 2 Place this value in equation (III) x + y = 5 ? x + 2 = 5 ? x = 5 - 2 ? x = 3 x= 3, y = 2 is the solution.
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