Question

On comparing the ratios a1/a2, b1/b2, c1/c2 find out wheather the lines responding the following pair of linear equation intersect at a point are parallel or coincident
a) 5x-4y+8=0
7x+6y-9=0

b) 6x-3y+10=0
2x-y+9=0​

Answer 1

Step-by-step explanation:

a) 5x - 4y + 8 =0

7x + 6y - 9 = 0

compare the equation

a1x + b1y + c1 =0

a2x + b2y + c2 = 0

a1 =5 , b1= -4 c1=8

a2 = 7 b2=6 c2= -9

a1/a2 = 5/7

b1/b2 = -4/6 =

c1/C2 = 8/-9

a1/a2 not equal to b1/b2

both are intersecting line at a point

.b) 6x - 3y + 10 = 0

2x - y + 9 = 0

compare the equation

a1x + b1y + c1 = 0

a2x + b2y + C2 = 0

therefore a1 = 6 , b1 = -3 , c1 = 10

a2 = 2 b2 = -1 , c2 = 9

a1 /a2 = b1/b2 = 3/1

b1 / b2 = -3/-1 = 1/2

c1/C2 = 12/24 = 1/2

therefore a1/a2 = b1/b2 not equal to c1/c2

hence lines are parallel

hope it is helpful... .