System equations - unique / no / infinite solution

[jwxie]

For example,

x + (alpha)y = 3
2x + y = 3

if alpha = 1, there is an unqiue solution.

then what value(s) of alpha will make the system returns no solution?

and what can we do to make this system infinite solution (if we only change the value of [3 3])

I don't know how to determine whether a system has unique / no / or infinite solution.

Thanks for any help.

 

[rochfor1]

Try writing it as a matrix and row-reducing.

 

[ZannX]

Put the coefficients into a 2x2 matrix.

If the determinant is 0 then the matrix is singular. A singular matrix can either have 0 solutions or infinitely many solutions.