Eliminating x and y

**scrible** · November 14th 2009, 07:17 PM

Hi there I have a problem that I am trying to figure out. It said that by eliminating $x$ and $y$ from the equations $\frac {1}{y}+\frac {1}{y}=1$ , $x +y = a$ , $\frac {y}{x}=m$ where $a =/0$ . obtain a relation between $m$ adn $a$ . Given that a is real, determine the ranges of values of $a$ for which $m$ is real. Can some one help me with this problem. Thank you in advance.

**TKHunny** · November 14th 2009, 07:24 PM

I'm guessing the first term should be 1/x rather than another 1/y?

Solve the second for x and substitute this expression into the other two equations. You'll be nearly done.

**scrible** · November 14th 2009, 07:40 PM

Originally Posted by TKHunny

I'm guessing the first term should be 1/x rather than another 1/y?

Solve the second for x and substitute this expression into the other two equations. You'll be nearly done.

I tried that and I am just not getting the problem solved at all.for the second I got $x=a-y$ but when I substitute that value for the other two eqaution every thing just seem confusing from there.

**topsquark** · November 14th 2009, 08:01 PM

Originally Posted by scrible

I tried that and I am just not getting the problem solved at all.for the second I got $x=a-y$ but when I substitute that value for the other two eqaution every thing just seem confusing from there.

Perhaps this is a bit sloppy (but then I tend to make problems a bit rougher than they need to be.) Start with the two equaitons:
$\frac{1}{x} + \frac{1}{y} = 1$
and
$x + y = a$

Then we know that
$\frac{x + y}{xy} = 1$

Put the second equation in:
$\frac{a}{x(a - x)} = 1$

or
$x^2 - ax + a = 0$

Now start from x + y = a and y = mx.
$x + mx = a$

giving
$x = \frac{a}{m + 1}$

Put this into the $x^2 - ax + a = 0$ equation to cancel the x and you are done.

-Dan

**scrible** · November 14th 2009, 09:41 PM

Originally Posted by topsquark

Perhaps this is a bit sloppy (but then I tend to make problems a bit rougher than they need to be.) Start with the two equaitons:
$\frac{1}{x} + \frac{1}{y} = 1$
and
$x + y = a$

Then we know that
$\frac{x + y}{xy} = 1$

Put the second equation in:
$\frac{a}{x(a - x)} = 1$

or
$x^2 - ax + a = 0$

Now start from x + y = a and y = mx.
$x + mx = a$

giving
$x = \frac{a}{m + 1}$

Put this into the $x^2 - ax + a = 0$ equation to cancel the x and you are done.

-Dan

Thank you very much

Thread: Eliminating x and y

LinkBack

Thread Tools

Display

Eliminating x and y

Similar Math Help Forum Discussions

Eliminating a variable in an LP problem

trig identities: eliminating θ

Eliminating the parameter when sin and cos are involved.

Eliminating the M2 in TI-30XA

Eliminating the arbitrary constants

Search Tags