Q. 13.9( 28 Votes )
The given equations are -
6x - 3y + 10 = 0
Divide the equation by 3 -
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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