Are Coupled Linear Equations Always Solvable Analytically?

[KFC]

I wonder if all coupling set of equations are not solvable analytically? I have a equation set as follows

y1 = a1*y1 + c1*y2;
y2 = a2*y2+ b2*y1 + c2*y3;
y3 = a3*y3+ b3*y2 + c3*y4;
y4 = a4*y4+ b4*y3 + c4*y5;
y5 = a5*y5+ b5*y4;

a's, b's and c's are constant. So is there any way to solve these equations?

 

[dacruick]

5 equations 5 unknowns. not to mention your last equation can be divided by y5

 

[KFC]

5 equations 5 unknowns. not to mention your last equation can be divided by y5

Sorry, some typo. I correct the equations.

 

[B-Con]

Sorry, some typo. I correct the equations.

You still have 5 equations and 5 unknowns. Look at Gauss-Jordan elimination, it's an algorithm that will spit out a solution.