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avatar+1616 

For certain values of k and m, the system

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

6a + 2b = k - 5a + mb + 17 - 11a + 18b

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

 Mar 17, 2024
 #1
avatar+128794 
+1

Simplify

 

10a - 3b  = 2

22a - (16+ m)b = 17+ k

 

Multiply  the first by  22  and the second by 10

 

220a  - 66b  =  44

220a - 10(16+m)b = 10(17+k)

 

To  have infinite solutions

 

10 (16 + m)  = 66   →  160 + 10m = 66 → 10m = -94  → m = -94/10  = -47/5

and

10(17 + k)  = 44   →  170 + 10k = 44 → 10k = -126 →  k = -126/10  = -63/5

 

cool cool cool

 Mar 17, 2024

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