Question

in equation a¹x+b¹y+c1=0 and a²x+b²y+c²=0 if a¹/a²=b¹/b²=c¹/c² them. a. unique solution. b.many solution c. no solution d. NOTA​

Answer 1

Answer:

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