1. ## system of equations

solve the system of equations where x,y are variables and a,b are constants:

x + y = a
(x^2)*y + x*(y^2) = b

2. Dear jmedsy,

$\displaystyle x+y=a$-------A

$\displaystyle (x+y)xy = axy$

$\displaystyle axy=b$--------B

By solving A and B you could easily get the answer.

3. Hello, jmedsy!

Straight substitution will solve it.

Solve the system of equations where $\displaystyle x,y$ are variables and $\displaystyle a,b$ are constants:

. . . $\displaystyle \begin{array}{cccc}x + y &= &a & [1] \\ x^2y + xy^2 &=& b & [2] \end{array}$

From [1], we have: .$\displaystyle y \:=\:a-x\;\;[3]$

Substitute into [2]: .$\displaystyle x^2(a-x) + x(a-x)^2 \:=\:b$

Expand: .$\displaystyle ax^2 - x^3 + a^2x - 2ax^2 + x^3 \:=\:b \quad\Rightarrow\quad ax^2 - a^2x + b \:=\:0$

Quadratic Formula: .$\displaystyle \boxed{x \;=\;\frac{a^2 \pm\sqrt{a^4-4ab}}{2a}}$

Substitute into [3]: .$\displaystyle y \;=\;a - \frac{a^2\pm\sqrt{a^4-4ab}}{2a} \quad\Rightarrow\quad\boxed{ y \;=\;\frac{a^2 \mp\sqrt{a^4-4ab}}{2a}}$

4. I get this answer. When I test the solutions in maple, they work in the first equation but not for the second.

nevermind i'm doing some really bizarre algebra. everything is ok now, thanks for the help

5. Mistaken post