system

k = -1, m = 8

For certain values of k and m, the system

3a + 2b = 2

6a + 2b = k + 3a + mb

has infinitely many solutions (a,b).  What are k and m?   

The problem states that  

                                                              6a + 2b  =  k + 3a + mb  

If you subtract 3a from both sides  

                                                              3a + 2b  =  k + mb  

The problem also states that  

                                                              3a + 2b  =  2  

From which it follows that  

                                                               k + mb  =  2  

Therefore  

                                                                       k  =  2 – mb  

and  

                                                                                2 – k 

                                                                       m  =  ———  

                                                                                   b 

_.

See this solution here:  https://web2.0calc.com/questions/need-help-with-system_6