Question 397526
The system can be represented in augmented matrix form:
{{{(matrix(2,3,1,5,4,2,b,c))}}}.
Multiplying the 1st row by -2 and then adding to the 2nd gives the new matrix

{{{(matrix(2,3,1,5,4,0,b - 10,c - 8))}}}

Hence for infinitely many solutions, b = 10 and c = 8;
for no solution, b = 10 and c not equal to 8;
for unique solution, b should be not equal to 10.