Solve an equation system

**Anna55** · February 26th 2011, 11:09 AM

Please solve this equation system:
x^2+xy=1/9
y^2+xy=1/16
Thank you!

**Ackbeet** · February 26th 2011, 11:13 AM

What ideas have you had so far?

**Anna55** · February 26th 2011, 10:12 PM

First i tried to square everything, however could not continue to solve it after that.
Later on I tried to factorize the first two terms in both equations, but I could not do this. My third attempt was to divide every term my x and use the substitution method. The last try was to use the substitution method directly.
All my attempts gave an incorrect answer or I was not able to continue.
Can you please help me?
Thank you!

**Prove It** · February 26th 2011, 10:33 PM

Rearrange equation 1:

$\displaystyle xy = \frac{1}{9} - x^2$

$\displaystyle xy = \frac{1 - 9x^2}{9}$

$\displaystyle y = \frac{1 - 9x^2}{9x}$ .

Now substitute this into the second equation and solve for $\displaystyle x$ ...

**Anna55** · February 26th 2011, 11:40 PM

Thank you prove it!
I substituted the value into the equation, however I did not get the correct answer. I got x=4/21, but the answer should be 4/15 or -4/15. Can you please show me how to solve it?

**lanierms** · February 27th 2011, 01:06 AM

$x^2+xy=\frac{1}{9}$ - - - - - - - - - - 1.

$y^2+xy=\frac{1}{16}$ - - - - - - - - - - 2.

From 1., we get $x(x+y)=\frac{1}{9}$

Therefore, $x+y=\frac{1}{9x}$

From 2., we get $y(x+y)=\frac{1}{16}$

Therefore, $x+y=\frac{1}{16y}$

So, $\frac{1}{9x}=\frac{1}{16y}$

$x:y=16:9$

Now, let's say that $x=16k$ , $y=9k$ .

From 1,. $16k(16k+9k)=\frac{1}{9}$

$k^2=\frac{1}{9\times16\times25}$

$k=\pm\frac{1}{60}$

So, $x=\pm\frac{4}{15}$ , $y=\pm\frac{3}{20}$ .

**Anna55** · February 27th 2011, 01:31 AM

Thank you very much lanierms!
I understand how to solve it now.

**HallsofIvy** · February 27th 2011, 02:46 AM

I hope you do. However, you should understand that you do not yet have the "solution". The problem does not ask for separate values of x and y but for pairs that satisfy the equation.

**Anna55** · February 27th 2011, 03:17 AM

I do not understand HallsofIvy. Can you please explain. When I look in the key, it shows x and y values as the answers.

Thread: Solve an equation system

LinkBack

Thread Tools

Display

Solve an equation system

Similar Math Help Forum Discussions

Solve an equation system with logarithms

solve an equation system!!!

[SOLVED] Equation system to solve

Solve the equation system

Use system of equation to solve

Search Tags