Question

given the linear equation 3x+4y=9. write another linear equation in these two variables such that the geometrical representation of the pair so formed is
1.intersecting lines 2.coincident lines

Answer 1

Answer:

1) Intersecting lines

a1/a2≠b1/b2

another equation can be:

5x-9y=2 ; 3x+4y=9 or

7x+5y=3 ; 3x+4y=9

2) coincident lines

a1/a2=b1/b2=c1/c2

another equation can be:

6x+8y=18 ; 3x+4y=9 or

9x+12y=27 ; 3x+4y=9

Answer 2

Answer:

1. Intersecting lines

x1/x2 ≠ y1/y2

Here, x1=3 and y1= 4

So, the second linear equation can be

3x-12y=26.

{Here, 3/3 ≠4/(-12)}

9x +7y = (-90)

{Here, 3/9 ≠ 4/7}

2. Coincident limes

x1/x2 = y1/y2 = constant1 / constant2

Here, x1=3, y1 = 4 and constant =(-9)

[Since + sign of 9 becomes - sign on transposing ]

So, the second linear equation can be

12x +16y=36 or 12x+16y-36=0

{Here 3/12 =4/16= 9/36}

-9x-12y=(-27) or -9x-12y+27=0.

{Here, 3/(-9)= 4/(-12)= 9/(-27)}