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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 \(3a + 2b - mb = k\).

 

Now, factor out b to get \(3a + (2-m)b = k\)

 

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

 

This means that \(2 -m = 2\), so \(\color{brown}\boxed{m = 0}\) and \(\color{brown}\boxed{k = 2}\)

 May 2, 2023

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