SOLUTION: Find two numbers whose sum is 23 and the difference of whose squares is 207

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Question 152193: Find two numbers whose sum is 23 and the difference of whose squares is 207
Answer by mducky2(62) About Me  (Show Source):
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Any problem which has two variables can only be solved if there are at least two equations.

Two numbers whose sum is 23:
x + y = 23

The difference of whose squares is 207: (Let's make x represent the larger of the two):
x2 - y2 = 207

Let's solve the first equation for x:
x + y = 23
x = 23 - y

Now we can plug it into the second equation:
x2 - y2 = 207
(23-y)2 - y2 = 207
232 - 46y + y2 - y2 = 207
529 - 46y = 207
529 - 207 - 46y = 207 - 207
322 - 46 y = 0
322 = 46y
322/46 = 46y/46
y = 7

Plugging into the first equation:
x = 23 - y
x = 16

Therefore, y = 7 and x = 16