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

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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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