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January 22nd, 2010, 01:53 PM   #1
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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.
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January 22nd, 2010, 02:17 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.
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January 22nd, 2010, 08:41 PM   #3
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Re: Solve a system of equations?

Using Cramer's rule:

Let

If t does not equal 0 then
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