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On comparing the ratios a 1 / a 2 , b 1 / b 2 and c 1 / c 2, find out whether the following pair of linear equations are consistent, or inconsistent (v) 4 / 3 x + 2 y = 8; 2y + 3y = 12

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 following pair of linear equations are consistent, or inconsistent

                (v)    \frac{4}{3}x + 2y = 8; \qquad 2x + 3y = 12

Answers (1)
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Given, Equations,

\\\frac{4}{3}x + 2y = 8; \qquad\\\\ 2x + 3y = 12

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{4/3}{2}=\frac{4}{6}=\frac{2}{3},\\\:\frac{b_1}{b_2}=\frac{2}{3}\:\:and\\\:\frac{c_1}{c_2}=\frac{8}{12}=\frac{2}{3}

As we can see 

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

It means the given equations have an infinite number of solutions and thus pair of linear equations is consistent.

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