Question

show that the following system of equations 3x+5y=12,5x+3y=4 has unique solution

Answer 1

The system of equations has unique solution if,
Ratio of coefficients of x is not equal to ratio of coefficients of y.

Now,
Coefficients of x = 3,5
Coefficients of y = 5,3

Now, 3/5 ≠ 5/3 .

Hence, The given system of equations have unique solutions

Answer 2

3x+5y=12
5x+3y=4

unique solution condition
a1/a2 is not equal to b1/b2 is not equal to c1/c2
3/5is not equal to 5/3 is not equal to 12/4

hope it help