Given,
$a–2b=6$……. (i)
$3a–6b=0$……. (ii)
From equation (i),
⇒ $b=(a–6)/2$
When $a=2$, we get $b=(2–6)/2=-2$
When $a=0$, we get $b=(0–6)/2=-3$
Thus, we have the following table giving Points on the line $a–2b=6$
| a | $2$ | $0$ |
| b | $-2$ | $-3$ |
From equation (ii),
Solve for b:
⇒ $b=a/2$
So, when $a=0$
$b=0/2=0$
And, when $a=2$
⇒ $b=2/2=1$
Thus, we have the following table giving Points on the line $3a–6b=0$
| a | $0$ | $2$ |
| b | $0$ | $1$ |
Graph of the equations (i) and (ii) is given below:
From the given graph, we can conclude that the two lines are Parallel to each other. So, the two lines do not intersect.
Thus, the given system has no solutions.