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 August 27th, 2014, 05:02 PM #1 Newbie   Joined: Aug 2014 From: England Posts: 14 Thanks: 0 Math Focus: Calculus Simultaneous Equations... Hi, I was wondering if somebody could help me with this question please! Show that the elimination of X from the simultaneous equations: x-2y = 1 3xy-y^2 = 8 Produces the equation: 5y^2+3y-8 = 0 Solve this quadratic equation and hence find the pairs of (x,y) for which the simultaneous equations are satisfied. Now the second part I can do easily, but eliminating X to produce the given equation is seeming to be rather difficult. Thank you!
 August 27th, 2014, 06:43 PM #2 Newbie   Joined: Aug 2014 From: England Posts: 14 Thanks: 0 Math Focus: Calculus Never mind I got it! It was actually quite simple haha. In case anybody is wondering... X - 2y = 1, so... X = 2y + 1 3y(2y+1)-y^2 = 8 6y^2+3y-y^2 =8 5y^2+3y=8 5y^2+3y-8 = 0
 August 28th, 2014, 02:55 AM #3 Senior Member   Joined: Apr 2014 From: Glasgow Posts: 2,164 Thanks: 736 Math Focus: Physics, mathematical modelling, numerical and computational solutions Well done! That method's called the substitution method, which is a nice method. The substitution method is also nice if you're given three equations and three unknowns (although your teacher may be a bit cruel to give you those kind of questions now!)

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# Solv simitaeonsly equation by elimination x-2y=1 -4y 3x =

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