Question

Show that if the linear equations x1 + kx2 = c and x1 + lx2 = d have the same solution set, then the equations are identical.

Answer 1

Let x2 = 0, then solution is (x1,0)
x1 = c
x1 = d
--> c = d
Now let x1 =0, then solution is (0,x2)
kx2 = c
lx2 = d
however c=d,
kx2 = lx2
--> k = l
Since the constants are shown to be equal, the equations are identical