Question 1023723
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The sum of two numbers is 9 and the difference of their squares is 9. Find the numbers.?
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<pre>
x + y = 9,        (1)
{{{x^2 - y^2}}} = 9.      (2)

Rewrite (2) in the form

(x+y)*(x-y) = 9,

then replace (x+y) by 9, due to (1). You will get

9*(x-y) = 9.

Next, reduce both sides by the factor 9. You will get

x - y = 1.        (3)

Now, you have thwo equations to solve,

x + y = 9,        (1')
x - y = 1.        (3')

Add them. You will get 2x = 9 + 10  --->  2x = 10  --->  x = {{{10/2}}} = 5.
Then from (1')  y = 9 - x = 9 - 5 = 4.

<U>Answer</U>.  x = 5, y = 4.
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