Math, asked by IMichUhKaran, 2 months ago

on comparing the ratio a1/a2, b1/b2 and c1/c2 find out weather the lines representing the following pairs of linear equation intersect at a point. are parallel or coincident
6x-3y+10=0
2x-y+9=0​

Answers

Answered by rk1252400
3

Answer:both lines are parallel

Step-by-step explanation:

(i) 5x – 4y + 8 = 0

7x + 6y – 9 = 0

Comparing these equation with

a1x + b1y + c1 = 0

a2x + b2y + c2= 0

We get

a1 = 5, b1 = -4, and c1 = 8

a2 =7, b2 = 6 and c2 = -9

a1/a2 = 5/7,

b1/b2 = -4/6 and

c1/c2 = 8/-9

Hence, a1/a2 ≠ b1/b2

Therefore, both are intersecting lines at one point.

(ii) 9x + 3y + 12 = 0

18x + 6y + 24 = 0

Comparing these equations with

a1x + b1y + c1 = 0

a2x + b2y + c2= 0

We get

a1 = 9, b1 = 3, and c1 = 12

a2 = 18, b2 = 6 and c2 = 24

a1/a2 = 9/18 = 1/2

b1/b2 = 3/6 = 1/2 and

c1/c2 = 12/24 = 1/2

Hence, a1/a2 = b1/b2 = c1/c2

Therefore, both lines are coincident

(iii) 6x – 3y + 10 = 0

2x – y + 9 = 0

Comparing these equations with

a1x + b1y + c1 = 0

a2x + b2y + c2= 0

We get

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

a2 = 2, b2 = -1 and c2 = 9

a1/a2 = 6/2 = 3/1

b1/b2 = -3/-1 = 3/1 and

c1/c2 = 12/24 = 1/2

Hence, a1/a2 = b1/b2 ≠ c1/c2

Therefore, both lines are parallel

Answered by Anonymous
60

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(iii) 6x – 3y + 10 = 0

2x – y + 9 = 0

Comparing these equations with

a1x + b1y + c1 = 0

a2x + b2y + c2= 0

We get:-

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

a2 = 2, b2 = -1 and c2 = 9

a1/a2 = 6/2 = 3/1

b1/b2 = -3/-1 = 3/1 and

c1/c2 = 12/24 = 1/2

Hence, a1/a2 = b1/b2 ≠ c1/c2

Therefore, both lines are parallel

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