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 January 22nd, 2010, 12:53 PM #1 Newbie   Joined: May 2008 Posts: 11 Thanks: 0 Solve a system of equations? OK, I know this can be done... I've seen the result. But I want to know HOW to solve the following for a, b, and c. ax1^2+bx1+c=y1 ax2^2+bx2+c=y2 ax3^2+bx3+c=y3 Of course, I am looking for solutions in terms of x and y - for example, I don't want something like a=bc^2-4x3, I'm looking for a=x3y2-3x1 - or whatever it really is.
January 22nd, 2010, 01:17 PM   #2
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Re: Solve a system of equations?

Quote:
 Originally Posted by Axle12693 OK, I know this can be done... I've seen the result. But I want to know HOW to solve the following for a, b, and c. ax1^2+bx1+c=y1 ax2^2+bx2+c=y2 ax3^2+bx3+c=y3 Of course, I am looking for solutions in terms of x and y - for example, I don't want something like a=bc^2-4x3, I'm looking for a=x3y2-3x1 - or whatever it really is.
You have three linear equations in three unknowns. It is a simple exercise to solve for a, b, and c.

 January 22nd, 2010, 07:41 PM #3 Senior Member   Joined: Feb 2009 From: Adelaide, Australia Posts: 1,519 Thanks: 3 Re: Solve a system of equations? Using Cramer's rule: Let $t= x_2x_3 [x_2-x_3] - x_1x_3 [x_1-x_3] + x_1x_2 [x_1-x_2]$ If t does not equal 0 then $c = ( y_1x_2x_3 [x_2-x_3] - x_1y_2x_3 [x_1-x_3] + x_1x_2y_3 [x_1-x_2] ) / t\\ b = ( y_1 (x_3^2-x_2^2) + y_2 (x_1^2-x_3^2) + y_3 (x_2^2-x_1^2) ) / t\\ a = ( y_1 [x_2-x_3] - y_2 [x_1-x_3] + y_3 [x_1-x_2] ) / t$

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