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.

Algebra ->  Matrices-and-determiminant -> 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.      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
The system can be represented in augmented matrix form:
%28matrix%282%2C3%2C1%2C5%2C4%2C2%2Cb%2Cc%29%29.
Multiplying the 1st row by -2 and then adding to the 2nd gives the new matrix
%28matrix%282%2C3%2C1%2C5%2C4%2C0%2Cb+-+10%2Cc+-+8%29%29
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.