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.


desmos-graph.png


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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