Question

ax+y=1
x+ay=b does it has a solution?

Answer 1

solve for y in the first equation. y = 1 - ax
x + a(1-ax) = b
x + a - a^2x = b
x( 1 - a^2) = b - a
x = (b-a) / ( 1 - a^2)
this has a solution as long as a is not equal to 1,-1 otherwise we have division by zero which is undefined

Answer 2

could you please use matrices to solve this question?