Question

On comparing the ratios a1/a2, b1/b2, c1/c2find out whether the lines representing thefollowing pairs of linear equations intersect at a point, are parallel or coincident:

a) 5x-4y+8=0 and, 7x+6y-9=0
b) 9x+3y+12=0 and, 18x+6y+24=0

Answer 1

Answer:

a) intersect at a point

b) coincident

Step-by-step explanation:

a) 5x-4y+8=0 and 7x+6y-9=0

here,

A1=5, B1= -4, C1=8

A2=7, B2=6, C1= -9

A1/A2=5/7,

B1/B2= -4/6= -2/3,

C1/C2=8/-9

5/7≠ -2/3

i.e. A1/A2≠B1/B2

so, the given pair of linear equations intersect at a point.

b)9x+3y+12=0 and 18x+6y+24=0

here,

A1=9, B1=3, C1=12

A2=18, B2=6, C2=24

A1/A2=9/18=1/2,

B1/B2=3/6=1/2,

C1/C2=12/24

1/2=1/2=1/2

9/18=3/6=12/24

i.e.

A1/A2=B1/B2=C1/C2

so, the given pair of linear equations is coincident.