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For certain values of k and m, the system

3a + 2b = 2

a + 2b = k - 8a - mb

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

 Jan 26, 2025
 #1
avatar+130466 
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Rearrange as

 

3a + 2b  = 2

9a + (2 + m)b  = k

 

We want the equations to match...multiply the first  equation by 3

 

9a + 6b = 6

 

Then

 

(2 + m)  = 6

m =4

 

And k =6

 

cool cool cool

 Jan 26, 2025

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