Thread: Confusing System of Equations

This is probably the hardest system of equations problem I have ever encountered.

"Consider the following system of equations x + y:
Ax+By=C
Dx+Ey=F

Where the constants A,B,C,D,E and F form an arithmetic sequence. How might you characterize the solutions to the system of equations?"

Originally Posted by bleacher39

This is probably the hardest system of equations problem I have ever encountered.

"Consider the following system of equations x + y:
Ax+By=C
Dx+Ey=F

Where the constants A,B,C,D,E and F form an arithmetic sequence. How might you characterize the solutions to the system of equations?"

If " A,B,C,D,E and F form an arithmetic sequence" then they have some "common difference" d. That is, B= A+ d, C= A+ 2d, D= A+ 3d, E= A+ 4d, and F= A+ 5d.

That's a cute problem! The answer is surprising.

Hllo, bleacher39!

Consider the following system of equations: .

. . where the constants form an arithmetic sequence.

How might you characterize the solutions to the system of equations?

Let the six coefficients be: .


The system becomes: .


Solve the system (use your favorite method): .


The solution is constant!