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  • On comparing the ratios a 1 / a 2 , b 1 / b2 and c 1 / c 2, find out whether the lines representing the following pairs of linear equations are consistent, or inconsistent:: (ii) 2x - 3y = 8 ; 4x - 6y = 9

Q3.    On comparing the ratios \frac{a_1}{a_2}, \frac{b_1}{b_2} and \frac{c_1}{c_2}, find out whether the lines representing the following pairs of linear equations are consistent, or inconsistent:

                    (ii)    2x - 3y = 8;\qquad 4x - 6y = 9

Answers (1)

best_answer

Given, Equations,

\\2x - 3y = 8;\qquad \\4x - 6y = 9

Comparing these equations with  a_1x+b_1y+c_1=0\:and\:a_2x+b_2y+c_2=0, we get 

\\\frac{a_1}{a_2}=\frac{2}{4}=\frac{1}{2},\\\:\frac{b_1}{b_2}=\frac{-3}{-6}=\frac{1}{2}\:and\\\:\frac{c_1}{c_2}=\frac{8}{9}

As we can see 

\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq\frac{c_1}{c_2}

It means the given equations have no solution and thus pair of linear equations is inconsistent.

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Pankaj Sanodiya

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