Question

if a pair of linear equations is given by a1x+b1y+c1= 0 and a2x+b2y+c2=0 the equations of these lines intersects.what is the nature of these equations​

Answer 1

Step-by-step explanation:

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

Answer 2

Answer:

This pair of linear equation given by a1x+b1y+c1= 0 and a2x+b2y+c2=0,

• a1/a2 ≠ b1/b2 ≠ c1/c2 if and only if lines are intersect and the nature of the roots unique solution
• a1/a2 = b1/b2 = c1/c2 for this coincident and infinitely many solutions
• a1/a2 = b1/b2 ≠ c1/c2 for this parallel and no solution.