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I need help solving the problem below.

For certain values of k and m, the system a + 2b = -3, 4a + 2b = k - a - mb has infinitely many solutions (a,b). What are k and m?

 Feb 19, 2024
 #1
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a + 2b = 3

5a + (2+ m)b = k 

 

This system will have infinite solutions when the equations are the  same

 

Multiply the first equation through by 5

 

5a + 10b  = 15

5a + (2 + m)b  =  k

 

This will  have infinite solutions when   m = 8  and  k  = 15

 

cool cool cool

 Feb 19, 2024

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