Question:Show that if the linear equations x1+k*x2=c and x1+l*x2=d have the same solution set, then the two equations are identical.(i.e. k=l and c=d)
My answer. for equation 1: x1=c-k*x2, let x2=t (t is a parameter), then x1=c-k*t for equation 2: x1=d-l*x2, let x2=t, then x1=d-l*t. if x1 and x2 are solutions for both equations 1 and 2,then c-k*x2=d-l*x2, and then here my question comes for I can find two situations,
1.c=d and k=l 2.c=3 d=4,k=2,and l=3,then x1=1 and x2=1 for equations 1 and 2.
That means even though c doesn't equal to d and k doesn't equal to l, these two equations still get the same solution set. Then how to prove it?