Question

For system of linear equations a1 x+ b1 y = c1 and a2 x+ b2 y = c2 which is incorrect
A. parallel if a1/a2 =b1/b2 =c1/c2
B coincident if a1/a2 =b1/b2 =c1/c2
C intersecting if a1/a2 does not equal to b1/b2
D No solution a1/a2 =b1/b2 but not equal to c1/c2​

Answer 1

Answer:

Correct option is

A

has a unique solution

A system of linear equations ax+by+c=0 and dx+ey+g=0 will have a unique solution if the two lines represented by the equations ax+by+c=0 and dx+ey+g=0 intersect at a point i.e., if the two lines are neither parallel nor coincident.

Essentially, the slopes of the two lines should be different.

Writing the equations in slope form we get

y=−

b

1

a

1

x

+

b

1

c

1

y=−

b

2

a

2

x

+

b

2

c

2

For a unique solution, the slopes of the lines should be different.

−

b

1

a

1



=−

b

2

a

2

b

1

a

1



=

b

2

a

2

Hence a

1

b

2



=a

2

b

1