Question

The lines represented by 2x+3y-9 = 0 and
4x+6y-18 = 0 are
a)Intersecting lines b) Coincident lines
c)Parallel lines d) perpendicular lines​

Answer 1

Answer:

these are coincident lines

Answer 2

Answer:

The correct answer is option(b) coincident lines

Step-by-step explanation:

Given,

2x+3y-9 = 0

4x+6y -18 = 0

Solution:

If Suppose $a_1x + b_1y + c_1 = 0$ and $a_2x + b_2y + c_2 = 0$ are a pair of linear equations, then they are  

intersecting lines if  $\frac{a_1}{a_2 } \neq \frac{b_1}{b_2}$

coincident lines if $\frac{a_1}{a_2 } = \frac{b_1}{b_2} = \frac{c_1}{c_2}$

Parallel lines if $\frac{a_1}{a_2 } = \frac{b_1}{b_2}$

Perpendicular if $\frac{a_1a_2}{b_1b_2} = -1$

Solution

Given equations 2x+3y-9 = 0 and 4x+6y-18 = 0

$a_1x + b_1y + c_1 = 0$ and $a_2x + b_2y + c_2 = 0$

$a_1$ = 2         $a_2$ = 4

$b_1$ = 3          $b_2$ = 6

$c_1$ = -9       $c_2$ = -18

$\frac{a_1}{a_2 } = \frac{b_1}{b_2} = \frac{c_1}{c_2} = \frac{1}{2}$

Hence the two lines are coincident lines

The correct answer is option(b) coincident lines

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