For which values parameter x,y system equations with two unknowns have unique solution,inconsistent or infinitely many solutions?

Question

Determine for which values parameter x,y system equations with two unknowns have unique solution,inconsistent or infinitely many solutions.

 ax+by=c^2

 a+x/b=b+y/a , a≠o,b≠o

 

and another equation:

 

x/a-p+y/b-p=1

x/a-q+y/b-y=1  a≠b,p≠q

 

 

 

Answer 1

Once you put a system of equations into a matrix [Ax|b] then you rref[Ax|b] on the bottom right you will either have 1=0, 0=1, 0=0

If you have a rref augmented matrix

1=0 unique

0=1 no sol

0=0 infinite sol

So put your matrix in full reduced form and look at the bottom right could look something like this

1 0 2 | 3

0 1 1 | 1

0 0 x | y

so when x=0, and y=0 we have infinite and so forth with the other combos.