For certain values of k and m, the system

a+2b=-3

4a+2b=k-a-mb

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

bluacijr Jul 21, 2024

#1**0 **

We get 3a + 2b = 2

6a + 2b = k - 3a - ab

Then we get 9a + (2 + m) * b = k

Equation first is equivalent to

9a + 6b = 6

There are an infinite number of solutions if second equation and third equation are equivalent. That is true only if the coefficients of b in both equations are the same and the constants in both are the same.

2+m = 6 --> m = 4

k = 6

ANSWERS: k = 6; m = 4

bader Jul 21, 2024