Question

On comparing the ratios of the cofficient , find out whether the pair of equation x-2y=O and 3x + 4y -20=0 is consistent or inconsistent?​

Answer 1

SOLUTION :

TO CHECK

On comparing the ratios of the coefficient to find

whether the pair of equation

x-2y= 0 and 3x + 4y -20=0

is consistent or inconsistent

CONCEPT TO BE IMPLEMENTED

A pair of Straight Lines

$\displaystyle \: a_1x+b_1y+c_1=0 \: and \: \: a_2x+b_2y+c_2=0$

is said to be inconsistent if

$\displaystyle \sf{ \: \frac{a_1}{a_2} = \frac{b_1}{b_2} \ne \:\frac{c_1}{c_2} }$

If the pair of Straight are not inconsistent then they are consistent

EVALUATION

Given pair of linear equations

$\sf{x - 2y = 0 \: \: \: and \: \: \:3x + 4y - 20 = 0 }$

Comparing with

$\displaystyle \: a_1x+b_1y+c_1=0 \: and \: \: a_2x+b_2y+c_2=0$

We get

$\displaystyle \sf{a_1 = 1 , b_1 = - 2, c_1= 0 \: \: and \: a_2 = 3 , b_2 = 4, c_2= - 20}$

Now

$\displaystyle \sf{ \: \frac{a_1}{a_2} = \frac{1}{3} }$

$\displaystyle \sf{ \frac{b_1}{b_2} = \:\frac{ - 2}{4} = - \frac{1}{2} }$

$\displaystyle \sf{ \frac{c_1}{c_2} = \frac{0}{ - 20} = 0 }$

Therefore

$\displaystyle \sf{ \: \frac{a_1}{a_2} \ne\frac{b_1}{b_2} \ne \:\frac{c_1}{c_2} }$

So the given pair of lines are not inconsistent

Hence the given pair of lines are consistent

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LEARN MORE FROM BRAINLY

Draw the graph of the linear equation

3x + 4y = 6

At what points, the graph cuts X and Y-axis

https://brainly.in/question/18185770