SOLUTION: Find the values of b and c for which the equations x+5y=4 and 2x+by=c have: A unique solution, an infinite set of solutions and no solution.

Question 397526: Find the values of b and c for which the equations x+5y=4 and 2x+by=c have:
A unique solution, an infinite set of solutions and no solution.
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
The system can be represented in augmented matrix form:
.
Multiplying the 1st row by -2 and then adding to the 2nd gives the new matrix

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.
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