Graphically, the pair of equations -

6x - 3y + 10 = 0

2x - y + 9 = 0

represents two lines which are

The given equations are -

6x - 3y + 10 = 0

Divide the equation by 3 -

…(i)

And 2x - y + 9 = 0 …(ii)

Let's find the x and y intercepts (point at which it touches x and y axis respectively) for both the lines -

For line = 0;

At x = 0, y = 10/3 (y - intercept),

So (0, 10/3) is a point in y axis.

At y = 0, x = - 5/3 (x - intercept)

And ( - 5/3, 0) is a point in x axis.

For line 2x - y + 9 = 0;

At x = 0 , y = 9 ( y - intercept ),

So (0,9) is a point in y axis.

At y = 0 , x = - 9/2 ( x - intercept )

And ( - 9/2,0) is a point in x axis.

Blue line represents

Red line represents 2x - y + 9 = 0

It is clear from the figure that the two lines are parallel.

(Also slope of the lines = = 2, which is the same)

Hence, the pair of equations represents two parallel lines.

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