SOLUTION: set up and solve the equations that fit the following: find the largest of two numbers such that the difference of twice the smaller and the larger number is negative two and thei

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Question 680111: set up and solve the equations that fit the following:
find the largest of two numbers such that the difference of twice the smaller and the larger number is negative two and their quotient is two fifths.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Two numbers, x is the largest, and y
:
find the largest of two numbers such that the difference of twice the smaller and the larger number is negative two
x - 2y = -2
:
and their quotient is two fifths.
x*y = 2%2F5
or
xy = .4
then
y = .4%2Fx
:
Replace y in the 1st equation
x - 2(.4/x) = -2
x - .8/x = -2
multiply by x
x^2 - .8 = -2x
a quadratic equation
x^2 + 2x - .8
Using the quadratic formula
x ~ -2.3416, find y: .4/-2.3416 ~ -.1708
and
x ~ +.3416, find y: .4/.3416 ~ +1.171
:
:
Check solution using the 1st solutions in the 1st equation
x - 2y = -2
-2.3416 - 2(-.1708) =
-2.3416 + .3416 = -2
:
You can check using the 2nd solutions in the 1st equation