Thread: simultaneous equations in matrices - 3 solutions

For what value(s) of will the system of equations,




have:

a) a unique solution?
b) no solution?
c) an infinite number of solutions?

Originally Posted by shawli

For what value(s) of will the system of equations,




have:

a) a unique solution?
b) no solution?
c) an infinite number of solutions?

Try solving it! For example, you can multiply the first equation by 2 and the second equation by m and subtract to eliminate y:





Now, if the denominator is not 0, there is a unique solution. If the denominator is 0 and the numerator is not, there is no solution. If both numerator and denominator are 0, there are an infinite number of solutions.