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August 27th, 2014, 05:02 PM   #1
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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!
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August 27th, 2014, 06:43 PM   #2
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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
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August 28th, 2014, 02:55 AM   #3
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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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