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?

Guest May 21, 2022

#1**0 **

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 \(k = 7 \times 6 = \color{brown}\boxed{42}\)

BuilderBoi May 21, 2022