Question

Say you have a linear system
2 * x1 + 4*x2 = f
c*x1 + d*x2= g
The system is consisten for all possible values of f and g. What can you say about the coefficients c and d.

Answer 1

Well because it says that it's consistent for all values of f and g this means that there is at least one solution or more for any given value of f and g. So this means that there will be one free variable and because of this c=2 and d=4. Is this wrong?

Answer 2

it could be but not always that means they can other values