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?
For a system of equations to have infinitely many solutions, the equations should be the same. We start by simplifying:
8a+b=−3
9a+(2−m)b=k
now we make the a terms the same:
8a+89∗(2−m)b=8k9
this means
8k9=−3,sok=−278
and
2−m=1,som=1
+400 
