Question

The equation x+2y=7 and ax+ay=b have no solution if

Answer 1

Answer:

IF A= 7, B= 1

Answer 2

Given : The equations x+2y=7 and ax+ay=b have no solutions  

To Find : Condition

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)

x+2y=7

ax+ay=b

will have no solution if  

1/a   =  2/a   ≠  7/b

1/a   =  2/a

is not possible  for any value of  a    

Hence  there is no such condition where equation does not have no solution

as 1/a   ≠ 2/a  Hence unique solution   for all value of a and b .

Understanding it in different way

linear Equation have no solution when they have same slope but different intercepts

x+2y=7  =>   y = -x/2 + 7/2  Hence slope = -1/2

ax + ay = b => y  = -x  + b/a   Hence slope = - 1

As slope of lines are different irrespective of the values of a and b

Hence lines would be intersecting and will have unique solution

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