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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?

 May 1, 2023
 #1
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Rewrite the second equation to 3a+2bmb=k.

 

Now, factor out b to get 3a+(2m)b=k

 

For the system of equations to have an infinite number of solutions, the 2 equations must be identical. 

 

This means that 2m=2, so m=0 and k=2

 May 2, 2023

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