Showing 2 simultaneous equations have a unique solution

by MathNovice   Last Updated August 12, 2018 12:20 PM

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

Pointers?



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