Question

The Resident Welfare Association of a Colony decided to build two straight paths in their neighborhood park such that they do not cross each other, to plant trees along the boundary lines of each path. One of the members of association Sarika suggested that paths should be constructed represented by the two Linear Equations x- 3y = 2 and -2x +6y = 5 . Check whether the two parts will cross each other or not.
(Class 10 Maths Sample Question Paper)

Answer 1

Given:

x -3y = 2
x -3y -2= 0……………..(1)

-2x +6y =5
-2x +6y -5=0……………(2)

On comparing the above equation with standard form of pair of  Linear Equations a1x + b1y +c1=0 and a2x + b2y +c2=0

Here, a1= 1, b1= -3 ,c1= -2
a2= -2, b2= 6 ,c2= -5

a1/a2= 1/-2 = -1/2, b1/b2= -3/6 = -½, c1/c2= -2/-5= 2/5

Here, a1/a2 = b1/b2 ≠ c1/c2

Hence, the paths represented by the equations are parallel(not intersect each other).

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Answer 2

x -3y = 2

x -3y -2= 0……………..(1)

-2x +6y =5

-2x +6y -5=0……………(2)

On comparing the above equation with standard form of pair of Linear Equations a1x + b1y +c1=0 and a2x + b2y +c2=0

Here, a1= 1, b1= -3 ,c1= -2

a2= -2, b2= 6 ,c2= -5

a1/a2= 1/-2 = -1/2, b1/b2= -3/6 = -½, c1/c2= -2/-5= 2/5

Here, a1/a2 = b1/b2 ≠ c1/c2

Hence, the paths represented by the equations are parallel(not intersect each other).

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