Question

determine whether the graph is intersecting, coinciding or parallel.

1. x+3y=9
6×+y=15

2. x+6y=4
2x+12y=8

3. x+4y=3
x+4y=5

4. 7x+2y=9
8x+y=2

5. x+y=10
5x+5y=50​

Answer 1

Step-by-step explanation:

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Answer 2

Given :  1. x+3y=9

6×+y=15

2. x+6y=4

2x+12y=8

3. x+4y=3

x+4y=5

4. 7x+2y=9

8x+y=2

5. x+y=10

5x+5y=50​

To Find : whether the graph is intersecting, coinciding or parallel.

Solution:

Pair of linear equations

a₁x  +  b₁y + c₁  =  0

a₂x  +  b₂y + c₂  =  0

Consistent

if a₁/a₂ ≠ b₁/b₂   (unique solution  and lines intersects each others) INTERSECTING

  a₁/a₂ = b₁/b₂ = c₁/c₂   (infinite solutions and line coincide each other )

COINCIDING

Inconsistent

if  a₁/a₂ = b₁/b₂ ≠  c₁/c₂  ( No solution , lines are parallel to each other)

PARALLEL

x+3y=9

6×+y=15

1/6  ≠ 3/1  

Hence INTERSCETING

x+6y=4

2x+12y=8

1/2 = 1/2 = 1/2

COINCIDING

x+4y=3

x+4y=5

1 = 1  ≠ 3/5

PARALLEL

7x+2y=9

8x+y=2

7/8 ≠ 2

INTERSCETING

x+y=10

5x+5y=50​

1/5 = 1/5 = 1/5

COINCIDING

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