How do you determine the solution in terms of a System of Linear Equations for 2x + 3y =5 and ax  y = 1?
1 Answer
This system has:
 No solution if
#a=2/3#  One solution :
#{(x=(8)/(23a)), (y=(25a)/(23a)):}# if#a!=2/3#
Explanation:
To find the connection between value of a parameter
It can be written as follows:
Let there be a system of 2 linear equations:
Let
Then the system has:
 One solution
#{(x=W_x/W),(y=W_y/W):} iff W!=0#  No solutions
#iff W=0# and#W_x!=0# or#W_y!=0#  Infinitely many solutions
#iff W=0# and#W_x=0# and#W_y=0#
This rule can be expanded for any system of

If
#W!=0# system has exactly one solution:#x_i=(W_{x_i})/W# for#1<=i<=n# 
If
#W=0# and any of#W_{x_i}# is not zero, then system has no solutions 
If
#W=0# and all#W_{x_i}# are zeros, then the system has infinitely many solutions.