SOLUTION: Consider the system of linear equations x + 3 y = a 2x + by = 8 where a and b are real numbers. I am asked to determine what values of a and b give a unique soluti

Algebra ->  Matrices-and-determiminant -> SOLUTION: Consider the system of linear equations x + 3 y = a 2x + by = 8 where a and b are real numbers. I am asked to determine what values of a and b give a unique soluti      Log On


   

Question 881132: Consider the system of linear equations
x + 3 y = a
2x + by = 8 where a and b are real numbers.
I am asked to determine what values of a and b give a unique solution.
If I am correct I know that b cannot equal 6. How do I prove this answer though?
Thank you
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
For infinitely many solutions, the second equation is a multiple of the first equation.
Multiply equation 1 by 2.
2x%2B6y=2a
So
6y=by or b=6
and
2a=8 or a=4
.
.
.
The other case is an inconsistent system that has no solution. That happens when
b=6 but a has any other value than a=4 because then the two lines are parallel.
.
.
.
So to have a unique solution, b can take on any value other than b=6
and a can take on any value.