Given this system of linear equations where {a} is parameter.for which value of a the system will have infinitely many solutions? step by step guide

I think your best bet is to eliminate y.  To do this, solve the 2nd equation for y and subst. the result into the first equation, replacing y:

                                                                   5(3-x)
5x + (a-1)y = 15 => (a-1)y = 5(3-x) => y =
                                                                     (a-1)

Substituting this result for y in the 2nd equation:
                      15-5x
5x + (a-1) * = 15
                        a-1

This can be simplified to 5x + 15 - 5x =15.

This equation is always true, for any x, for almost any a.  Note that a cannot equal 1, because that would produce division by zero.

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