Thread: 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.

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.

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.

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.