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

Question 152193: Find two numbers whose sum is 23 and the difference of whose squares is 207
Answer by mducky2(62) (Show Source): You can put this solution on YOUR website!
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

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