For certain values of k and m, the system

3a + 2b = 2

a + 2b = k - 8a - mb

has infinitely many solutions (a,b). What are k and m?

Stanry Aug 18, 2024

#1**0 **

In order to have an infinite number of solutions, we want two equivalent equations

Subtracting 3a from both sides gives us 3a+2b=k+mb.

Because we want both equations to be equal to each other (meaning the left side matches), we can incorporate the equation k+mb=2

We want M to be an integer-- other than zero (except it cannot be other than zero because we want the equations to line up)

We need m=0 so K would have to be 2

M=0

K=2

lonelychungus Aug 18, 2024