Solving Simultaneous Equations with 2xy: Tips and Methods

AI Thread Summary
To solve the simultaneous equations x = 3x^2 + 2xy and y = x^2 + 3y + 8, factor the first equation to get x(1 - 3x - 2y) = 0, which allows for splitting the equation based on the zero product property. The second equation is linear in y, making it suitable for substitution to find y in terms of x. After isolating variables, substitute back to find the values of both x and y. This method effectively addresses the complexity introduced by the 2xy term. Understanding these steps can simplify solving similar simultaneous equations.
jimmy42
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I have the following simultaneous equations. However I am unsure how to handle that 2xy. Can someone give a pointer to any known methods?

x= 3x^2+2xy
y=x^2+3y+8
 
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Just factor out the first equation so you can get x(1-3x-2y)=0 and then you transform the equation.
 
Second equation is linear in y, so you can solve by substitution.
 
After you have x(1-3x-2y)=0, you will then have to split that up with what you know about a*b=0.
 

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