For a certain value of k, the system
3a + 4b = 7 + 2a
6a + 4b = k - 20b
has infinitely many solutions (a, b). What is k?
+2666 Simplify both equations to:
\(a + 4b = 7\)
\(6a + 24b = k\)
Note that the second equation is 6 times the first. For a system to have an infinite amount of solutions, the equations must be multiples of each other.
This means that \(k = 7 \times 6 = \color{brown}\boxed{42}\)
