Question

Give graphical representation of equation:a1x+b1y=c1 & a2x+b2y=c2

Answer 1

Answer:

In case of infinite many solutions ratio of the coefficients of the equations must be same.

Thus for the equations too have infinite solutions taking the ratios we get the condition

a

2

a

1

=

b

2

b

1

=

c

2

c

1

Answer 2

Answer:

Given : The graphical representation of pair of linear equations

a₁x  +  b₁y + c₁  =  0  and a₂x  +  b₂y + c₂  =  0   area parallel lines

To Find :  . How many solutions do these equations have?​

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)

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

Inconsistent

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

The graphical representation of pair of linear equations

a₁x  +  b₁y + c₁  =  0  and a₂x  +  b₂y + c₂  =  0   area parallel lines

Hence they never  meet each other

so there is no solution

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Step-by-step explanation: