Simultaneous Equation

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November 6th 2011, 01:43 PM
jacobjacob44

Simultaneous Equation

Hi, I have been given a homework by my teacher to solve the following equations. I have the answers for the question but all of my attempts at them have ended up in completely the wrong answers.
The answers for the questions are x = -1, y = -3 OR x = 1, y = 3
The equations are:
$y=3x$
$2y^2-xy=15$
Probably very simple but I've hit a block and cant manage to work it out.
November 6th 2011, 01:56 PM
HallsofIvy

Re: Simultaneous Equation

Well, what have you tried? If you replace "y" in the second equation by "3x", you get a very simple quadratic equation in x alone. What quadratic equation and how do you solve it?
November 6th 2011, 02:16 PM
jacobjacob44

Re: Simultaneous Equation

I tried subbing 3x in as Y.
Ended up something like:
$2(3x)(3x)-3x^2=15$
$6x^2-3x^2=15$
$6x^2-3x^2-15=0$
But I then dont know where to go from there, or if the answers are ever right.
November 6th 2011, 02:40 PM
skeeter

Re: Simultaneous Equation

$y = 3x$

$2y^2 - xy = 15$

substitute $3x$ for $y$ in the second equation ...

$2(3x)^2 - x(3x) = 15$

mind your order of operations ...

$18x^2 - 3x^2 = 15$

$15x^2 - 15 = 0$

$15(x^2-1) = 0$

$15(x-1)(x+1) = 0$

finish it

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