+0  
 
0
3
1
avatar+729 

For certain values of $k$ and $m,$ the system
a + 2b = -3 - 7a + b,
4a + 2b = k - 5a - mb
has infinitely many solutions $(a,b).$ What are $k$ and $m?$

 Jun 15, 2024
 #1
avatar+129733 
+1

Simplify as

 

8a + b = -3

9a + (2 +m)b = k 

 

This will have infinte solutions when the equations are the  same...so....multiply the first equation  by 9 and the  second by 8 and  we  get

 

72a + 9b = -27

72a + 8 (2 + m)b = 8k

 

So

 

9 = 8(2 + m)            and          8 k  = -27

9 = 16 + 8m                              k = -27/8                           

-7 = 8m

m = -7/8

 

cool cool cool

 Jun 15, 2024

1 Online Users