# Please help with this Q about simultaneous equations

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• Feb 27th 2013, 02:00 AM
James7361539
Please help with this Q about simultaneous equations
Hi I have to solve a really hard simultaneous equation and I don't know how to do it.

Please note it has p1,p2,p3,q1,q2,q3. The numbers are subscripts.
These all represent constant values. That is they are not variables.
The two variables are x and y.

1. x(q2+q3-2q1)-y(p2+p3-2p1)+(q1p2-p1q2)+(q1p3-q3p1)=0
2. x(2q2-q1-q3)-y(2p2-p1-p3)+(p2q1-q2p1)+(p2q3-q2p3)=0

I have tried to solve this by re-arranging then subbing in but this quickly gets out of hand as the subbed in equation is very long and
it does not lead to the correct answer.

Thanks in advance for replies.
• Feb 27th 2013, 03:31 AM
a tutor
Re: Please help with this Q about simultaneous equations
Quote:

Originally Posted by James7361539
Hi I have to solve a really hard simultaneous equation and I don't know how to do it.

Please note it has p1,p2,p3,q1,q2,q3. The numbers are subscripts.
These all represent constant values. That is they are not variables.
The two variables are x and y.

1. x(q2+q3-2q1)-y(p2+p3-2p1)+(q1p2-p1q2)+(q1p3-q3p1)
2. x(2q2-q1-q3)-y(2p2-p1-p3)+(p2q1-q2p1)+(p2q3-q2p3)

I have tried to solve this by re-arranging then subbing in but this quickly gets out of hand as the subbed in equation is very long and
it does not lead to the correct answer.

Thanks in advance for replies.

Those aren't equations.
• Feb 27th 2013, 03:41 AM
James7361539
Re: Please help with this Q about simultaneous equations
Quote:

Originally Posted by a tutor
Those aren't equations.

Sorry I forgot the =0 at the end of them
I have edited my post now.
• Feb 27th 2013, 05:04 AM
HallsofIvy
Re: Please help with this Q about simultaneous equations
So, essentially, you have Ax+ By= C and Dx+ Ey= F. Multiply the first equation by E, the second equation by B, and subtract:
(AE- BD)x= CE- BF, x= (CE- BF)/(AE- BD).

Multiply the first equation by D, the second equation by A, and subtract:
(BD- AE)y= CD- AF, x= (CD- AF)/(BD- AE).

Now replace A, B, C, D, E, and F with those complicated expressions.