Expert: Paul Klarreich - 11/24/2009

Question
Question : For what values of A and B , the simultaneous equations

x + y + z = 6
x + 2y + 3z = 10
x + 2y + Az = B

have
-no solution
-a Unique solution
-an Infinite number of solutions

Answer
Questioner: varunnayudu
Country: India
Category: Advanced Math
Private: Yes   << changed.
Question : For what values of A and B , the simultaneous equations

x + y + z = 6
x + 2y + 3z = 10
x + 2y + Az = B

have
-no solution
-a Unique solution
-an Infinite number of solution
.................................
You didn't tell me what you are studying, so I will have to guess.

Find the determinant of the left side.  It will depend on A.

Find the value of A that makes it zero.

All other values of A lead to a unique solution, so use that value of A to:

Find a linear combination of the first two equations (left sides only) that yield the third (using your A).

Then if B is the correct right side for that l.c., you have an infinite number of solutions.  Otherwise, none.