My Math Forum simultaneous equations anyone?

 Algebra Pre-Algebra and Basic Algebra Math Forum

 August 28th, 2009, 12:16 PM #1 Senior Member   Joined: Jul 2009 Posts: 136 Thanks: 0 simultaneous equations anyone? OK, I got this one I believe. y/2 - x = 2, 6x - 3y/2 = 3 and I ended up with y = 10, x = 3. But these two are giving me fits: x/2 - y/5 = 1, y - x/3 = 8. I started by simplifying the y as y = 8 + x/3 and substituting that into the other "y" that would present itself as: x/2 - 8/5 + x/3/5 = 1. The "x/3/5" should be read as x/3 as the numerator and 5 as the denominator. So I suppose I need to know if that is correct as a start. Let me know, thanks! IF you can go further with it, then that would be great.
 August 28th, 2009, 12:57 PM #2 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,805 Thanks: 1045 Math Focus: Elementary mathematics and beyond Re: simultaneous equations anyone? I did it this way: x/2 - y/5 = 1, y - x/3 = 8 ? 10(x/2 - y/5) = 10, 3(y - x/3) = 24 ? 5x - 2y = 10, 3y - x = 24 . . . . and so on . . . .
 August 28th, 2009, 04:34 PM #3 Senior Member   Joined: Apr 2007 Posts: 2,140 Thanks: 0 Since $\frac{x}{2}\,-\,\frac{y}{5}\,=\,1$ is equivalent to saying that $y\,=\,\frac{5}{2}x\,-\,5$, and $y\,-\,\frac{x}{3}\,=\,8$ is equivalent to saying that $y\,=\,\frac{x}{3}\,+\,8,$ since $y\,=\,y$ is obvious, the equation $\frac{5}{2}x\,-\,5\,=\,\frac{x}{3}\,+\,8$ is true, and solving the equation gives us $x\,=\,6,$ and we will use this $x$ value to determine the obvious of $y\,=\,10.$
 August 30th, 2009, 04:25 AM #4 Senior Member   Joined: Jul 2009 Posts: 136 Thanks: 0 Re: simultaneous equations anyone? Thanks everyone! Wouldn't you know that the very next day I got it! y = 8 + x/3 as noted earlier and then I followed it up by simplifying: 5x/10 - 16 - 2x/3 /10 = 1... 5x - 16 - 2x/3 = 10... 15x/3 - 16 - 2x/3 = 10... 15x/3 - 2x/3 = 26... 13x/3 = 26... 13x = 78... x = 6... I appreciate your help and assistance.... Have been enjoying the problems!
 August 30th, 2009, 04:28 AM #5 Senior Member   Joined: Apr 2007 Posts: 2,140 Thanks: 0 IMO, equations are fun to study!

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