Let a, b, c and d be real numbers that are not all zero. Let ax + by = p cx + dy = q be a pair of equations in the variables x and y with p, q ∈ R.
Show this system of equations has a unique solution if and only if ab − cd != 0.
From Determinant of coefficient matrix, I know (ad -bc) =0 => no unique solution. Have tried substitution of one equation into another and replacement.
=> ab = cd....show that solution is unique
<= solution is unique ....show that ab - cd != 0