+1765 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?
+129845 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
