Question:
Graphically, the pair of equations
6x – 3y + 10 = 0
2x – y + 9 = 0
represents two lines which are
(a) intersecting at exactly one point
(b) intersecting exactly two points
(c) coincident
(d) parallel
Solution:
The given equations are
$6 x-3 y+10=0$
$\Rightarrow 2 x-y+\frac{10}{3}=0$ [dividing by 3 ]... (i)
and $\quad 2 x-y+9=0$ .......(ii)
Now, table for $2 x-y+\frac{10}{3}=0$,
and table for $2 x-y+9=0$,
Hence, the pair of equations represents two parallel lines.