Multiply left handside of equation one by xy, RHS by 5. (since xy=5 we can do this and equality still holds).
We get 2y +3x = 20
Here's a question on my GMAT study book that I really don't know how to figure out...
Could someone show me HOW to work this out? And/Or the most effective way to figure it out?
if --- + --- = 4 and xy = 5, then 3x + 2y = ?
crap, the formatting isn't there...
if (2/x) + (3/y) = 4 and xy = 5, then 3x + 2y
is there somewhere I can plug this into to see the entire problem worked out? that's the only way i'm going to be able to figure this out without a math wiz sitting right next to me.
a? b? c?
we're dealing with x & y here...
what's this mean:b=c
"That is an absolute crippler, if you don't know that you will die at a young age."
The a,b,c stuff was just showing how you manipulate equations.
You have to do the same thing to both sides, otherwise the equality doesn't hold.
x=y implies x+5=y+5
x=y implies 3x=3y
x + y = 6 implies 6(x+y)=6*6 implies 6x + 6y = 36
Absolutely crucial you understand the above or you will never ever be able to solve any maths problems.
In your second line you wrote:
2/x + 3/y = 4 implies 3/x + 3/y = 4xy
This is not true.
You should have written:
2/x + 3/y = 4 implies (2/x + 3/y)xy = 4xy
The whole problem, with the logic written between lines:
1. 2/x + 3/y = 4
2. xy = 5
2/x + 3/y = 4
(since a=b implies ac = bc)
=>(2/x + 3/y)xy = 4xy
(since a(b+c) = ab +ac)
=> 2xy/x + 3xy/y = 4xy
(since a/a = 1)
=> 2y + 3x = 4xy
(since xy = 5 from equation 2)
=> 2y + 3x = 4*5
=> 2y + 3x = 20