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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?

 Jun 10, 2023
 #1
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Well, first of all, we can simplify the bottom equation:

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

into 

3a + 2b = k + mb

Because the top equation is also 3a+2b, and the bottom is also 3a+2b, and there are infinitely many solutions, that means:

k+mb = 2

And because b can be anything, that means m has to be 0 to work. that means k = 2

 

k = 2

m = 0

 Jun 10, 2023

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