For a certain value of k, the system
3a + 4b = 7,
6a + 4b = k - 3a - 8b
has infinitely many solutions (a,b). What is k?
3a + 4b = 7 ⇒ multiply through by 3 ⇒ 9a + 12b = 21
6a + 4b = k - 3a - 8b ⇒ simplify ⇒ 9a + 12b = k
k = 21
