Given the linear equation (2x+3y-8=0), write another linear equation in two variables such that the geometrical representation of the pair so formed is:
(i) Intersecting lines (ii) Parallel lines
(iii) Coincident lines
Solution (i)
Let the second line be equal to
Comparing given line (2x+3y-8=0) with
, we get
and
Two lines intersect with each other if
So, second equation can be (x+2y=3) because
We can verify this graphically.
We can plot both of the lines to show that they are intersecting:
(Blue) and
(Red)
Solution (ii)
Let the second line be equal to
Comparing given line (2x+3y-8=0) with
, we get
and
Two lines are parallel to each other if
So, second equation can be (2x+3y-2=0) because
We can verify this graphically.
We can plot both of the lines to show that they are parallel.
(Blue) and
(Red)
We can clearly see that two lines are parallel to each other.
Solution (iii)
Let the second line be equal to
Comparing given line (2x+3y-8=0) with
, we get
and
Two lines are coincident if
So, second equation can be (4x+6y-16=0) because
We can verify this graphically.
We can plot both of the lines to show that they are coincident.
(Blue) and
(Red)
We can clearly see that the lines are coincident.
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