Question

the pair of equations x+y=1 and x+y=-5 has how many solutions​

Answer 1

$\Huge{\textbf{\textsf{{\purple{Ans}}{\pink{wer}}{\color{pink}{:}}}}}$

$</p><p>If\\</p><p>a_1x + b_1y + c_1 = 0 \:\:\:and \\</p><p>a_2x + b_2y + c_2 = 0 \:\:are \: two \: equations\:\:then \\</p><p>they \:have \: no \: \: solution \: \: if \\ \\ \frac{a_1}{a_2} \:= \: \frac{b_1}{b_2} </p><p> \\ \implies\:\frac{1}{1} \:\:=\: \: \frac{ 1}{1} \\ \implies\:1 \:=\: 1$

so they have no solution.

They are parallel. So they have no intersection points.

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  ≠ 1/15

Hence no solutions   , lines are parallel to each other

Correct Answer is No solution

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