Question

on comparing the ratio a1/a2,b1/b2,c1/c2
find out whether the lones representing the following pairs of linear equations intersect at a point or parallel or coincide
3x+6y-5=0
6x+12y-10=0​

Answer 1

$\huge\bf{Answer:-}$

Given :-

The equation is -

• 3x + 6y -5 =0
• 6x + 12y -10 =0

To find :-

Whether The above linear equation is unique solution , No solution or Infinitely many solution

$\underline\bold{Solution:-}$

The equation is -

• 3x + 6y -5 =0
• 6x + 12y -10 =0

Here,

a1 = 3 , b1 = 6 , c1 = -5

a2 = 6 , b2 = 12, c2 = -10

so,

$\frac{a1}{a2} = \frac{3}{6} =\frac{1}{2}$

$\frac{b1}{b2} = \frac{6}{12} =\frac{1}{2}$

$\frac{c1}{c2} = \frac{-5}{-10} =\frac{1}{2}$

As , $\frac{a1}{a2} = \frac{b1}{b2} = \frac{c1}{c2}$

so, It has infinitely many solution

$\therefore{They \:Coincide \:each \:Other}$

★Note:-

• when a1/ a2 ≠ b1 / b2 then it will be unique solution means the lines will intersect at a single or one point.

• when a1 / a2 = b1/b2 ≠ c1/c2 then it will have No solution means the lines fromed by the equation will be parallel to each other.

• when a1 /a2 = b1/b2 = c1/c2 then it will have infinitely many solution means the lines will coincide with each other .