Question

a which of the following pairs of linear equations has Lunique solution no Solution infinitely many solutions Case there is a unique solution, find it by using Cross multiplication method. 3x + 4y - 10 = 0 In 3x +4y-15=0
​

Answer 1

Answer:

x–3y–3=0

3x–9y–2=0

Comparing these with pair of equations of the form a

1

x+b

1

y+c

1

=0

and a

2

x+b

2

y+c

2

=0,

a

2

a

1

=

3

1

,

b

2

b

1

=

−9

−3

=

3

1

,

c

2

c

1

=

2

3

∵

a

2

a

1

=

b

2

b

1



=

c

2

c

1

, the lines have no solution.

(ii) 2x+y=5

3x+2y=8

a

2

a

1

=

3

2

,

b

2

b

1

=

2

1

,

c

2

c

1

=

8

5

∵

a

2

a

1



=

b

2

b

1

, the lines have unique solution.

(iii) 3x−5y=20

6x−10y=40

a

2

a

1

=

6

3

=

2

1

,

b

2

b

1

=

−10

−5

=

2

1

,

c

2

c

1

=

40

20

=

2

1

∵

a

2

a

1

=

b

2

b

1

=

c

2

c

1

, the lines have infinitely many solution.

(iv) x−3y−7=0;3x−3y−15=0

a

2

a

1

=

3

1

,

b

2

b

1

=

−3

−3

=1,

c

2

c

1

=

15

7

∵

a

2

a

1



=

b

2

b

1

, the lines have unique solution.