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Find two numbers such that the smaller subtracted from the larger is 9 and
the difference of the square of the larger subtracted from square of the smaller is 9.
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The correct answer is 4 and -5.
Both @greenestamps and @josgarithmetic produced wrong solutions and wrong answers.
You are gven that
a - b = 9 (1) (where "a" is the larger number)
b^2 - a^2 = 9 (2)
From eq(2), you have
(b-a)*(a+b) = 9. (3)
In (3), replace (b-a) by -9, since it is given (see (1) ). You will get
(-9)*(a+b) = 9, or
a + b = -1.
Thus you have this system of two linear equations
a - b = 9, (1)
a + b = -1 (4)
Add them. You will get
2a = 9 + (-1) = 8 ====> a = 8/2 = 4.
Then from eq(4), b = -1 - 4 = -5.
Check. b^2 - a^2 = (-5)^2 - 4^2 = 25 - 16 = 9. ! Correct !