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plz help with systems

 

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?

 Jul 3, 2023
 #1
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Adding  3a+mb to both sides of the second equation, we have
3a+2b=2
9a+(m+2)b=k
We multiply the first equation by 3, in order to make the coefficient of a equal to 9:
9a+6b=6
9a+(m+b)b=k
This system will have infinitely many solutions when both equations are the same. This occurs when k=6 and m+2=6.... 
im sure you can figure out what m is :)))

 Jul 4, 2023

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