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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:: (iii) 3 / 2 x + 5 / 3 y = 7 ; 9x - 10y = 17

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:

                    (iii)    \frac{3}{2}x + \frac{5}{3}y = 7;\qquad 9x -10y = 14

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Given, Equations,

\\\frac{3}{2}x + \frac{5}{3}y = 7;\qquad\\ \\ 9x -10y = 14

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{3/2}{9}=\frac{3}{18}=\frac{1}{6},\\\:\frac{b_1}{b_2}=\frac{5/3}{-10}=\frac{5}{-30}=-\frac{1}{6}\:and\\\:\frac{c_1}{c_2}=\frac{7}{14}=\frac{1}{2}

As we can see 

\frac{a_1}{a_2}\neq\frac{b_1}{b_2}

It means the given equations have exactly one solution and thus pair of linear equations is consistent.

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