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avatar+555 

For certain values of k and m, the system

3a + 2b = 12 - 5a + 7b

8a + 6b = k - a - mb

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

 Mar 22, 2024
 #1
avatar+128406 
+1

Simplify as

 

8a - 5b =   12

9a +(6 + m)b = k

 

Multiply the first  equation by 9  and the  second by 8

 

72a  - 45b =  108

72a + 8(6+m) =  8k

 

To have infinite solutions  both of these must be true

 

8 (6 + m)  =  -45

48 + 8m = -45

8m = - 93

m = -93 / 8  

 

and

 

8k = 108

k = 108 / 8  =   27 / 2

 

 

cool cool cool

 Mar 22, 2024

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