Math Is Fun Forum

gyanshrestha

Member

Registered: 2007-11-06

Posts: 41

how to solve

x(x+y)=205
y(x-y)=35

i have solve it but i want tricky answer or solving method.
plz help me

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Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,395

Re: how to solve

Part I:-
Add the two equations after multiplying the second by -1.
x²+y²=170............(1)
Add 2xy to both sides,
x²+y²+2xy=170+2xy.......(1A)
Part II:-
Multiply the two equations:
xy(x²-y²)=205*35...........(2)
Divide (1A) by (2)
(x+y)(x+y)/xy(x+y)(x-y) = (170+2xy)/(205*35)
=>(x+y)/(x-y)xy = (170+2xy)/205*35
=>(x+y)/(x-y) = (170xy+2x²y²)/205*35

Part III : Divide the first equation given by the second.
(x/y)[(x+y)/(x-y)]=205*35=41/7
=>(x/y)(170xy+2x²y²)/205*35=41*7
=>(x/y)(170xy+2x²y²)/41*7=41*7
=>(170x²+2x³y)/y=41*7*41*7=1681*49
=>x²(170+2xy)/y=1681*49
=>x²(x+y)²/y=1681*49
=>205*35/y=1681*49
=>y=205*35/1681*49=5*7/41*7=35/287

I know I am wrong, but I am unable to find out where I have gone wrong!

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gyanshrestha

Member

Registered: 2007-11-06

Posts: 41

Re: how to solve

x^2 + y^2 = 170, which is a circle centred about the origin with radius root(170). This has an infinite number of solutions.

the equations given are of two variable and for two variable equation only two equation of different condition are required
Given equations are sufficient for finding the value of  x and y.

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Daniel123

Member

Registered: 2007-05-23

Posts: 663

Re: how to solve

Complete the square on one of the equations to isolate x / y?

TheDude

Member

Registered: 2007-10-23

Posts: 361

Re: how to solve

I think substitution would be more useful here.

You can factor this into the form (2y^2 - a)(y^2 - b) = 0, from which you can easily solve for y and then x.  a and b are irrational, which means x and y are too, and I'm too tired to deal with irrational numbers right now, but that should be good enough for you to take over.

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Wrap it in bacon

csg48

Guest

Re: how to solve

You have 70% solution and 50 liters of 40% solution.  How many liters of 70% solution do you need to add to the 40% solution to have a 50% solution.  My son and I did others that were simular it was set up as x+y=a known number.  Not with the known number in the center.  This is as far as I was able to get.  Am I starting out wrong?

70% + 40% = 50%

x      + 50 =    y

.7x  +   .4(50)  = .5y

.7x  +  20  = .5y

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: how to solve