Is there solution for this kind of equation

[mist]

to solve this question is possible or not

X1Y1 = A

X2Y2 = B

X3Y3 = C

X4Y4 = D

X4Y5 = E

HERE A,B,C,D, and E known. X and Y ` s unknown. if you divide

X1Y1 / X2Y2 = A/B
X1Y1 / X3Y3 = A/C
X1Y1 / X4Y4 = A/D
X1Y1 / X5Y5 = A/E
X2Y2 / X3Y3 = B/C
X2Y2 / X4Y4 = B/D
X2Y2 / X5Y5 = B/E
X3Y3 / X4Y4 = C/D
X3Y3 / X5Y5 = C/E
X4Y4 / X5Y5 = D/E

we have 10 equation and 10 unknown, may I ask can we find each X and Y values. is iy possible.

thanks

 

[arunbg]

By X1, I assume you mean X₁ and similarly for the rest. Each of your original equations are independent of each other.
In the derived equations, even though you seem to have 10 independent equations and 10 unknowns, when solving you will find that these are in fact dependent, therefore a solution is not possible.

 

[CompuChip]

To show arunbg's point: if you divide the last two equations,
X3Y3 / X5Y5 = C/E
X4Y4 / X5Y5 = D/E
you get
X3Y3 / X4Y4 = C/D
which is already in the list.
No matter how you rewrite it, you will keep 5 independent equations for the 10 unknowns.