Consistency in Linear Equations: The Relationship Between Coefficients c and d

[cmajor47]

Homework Statement

Suppose the system below is consistent for all possible values of f and g. What can you say about the coefficients c and d?

Homework Equations

x₁ + 3x₂ = f
cx₁ + dx₂ = g

The Attempt at a Solution

I really just have no idea what this says about c and d.

 

[Dick]

Try solving the equations. Multiply the first one by c and subtract them and solve for x2. What could go wrong with this procedure?