Question

how many solution does the pair of equations x+y=1 and x+y=5 have?​

Answer 1

Answer:

$\blue{no \: solution}$

Reason:-

$\mathfrak {\frac{a1}{a2} = \frac{b1}{b2} \: not \: equal \: to \: \frac{c1}{c2} }$

Answer 2

Given : pair of equations   x+y=1 and x+y=5

To Find : how many solution  

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+y=1  

x+y=5

1/1  = 1/1  ≠ 1/5

Hence no solutions   , lines are parallel to each other

Correct Answer is No solution

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