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?
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
+2653 
