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)/(2-3a)), (y=(-2-5a)/(2-3a)):}# 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.