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# On comparing the ratios a 1 by a 2 , b 1 by b2 and c 1 by c 2, find out whether the lines representing the following pairs of linear equations are consistent, or inconsistent:: (i) 3x plus 2y equals 5 ; 2x minus 3y equals 7

Q2.    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:

(i)    $3x + 2y = 5;\qquad 2x - 3y = 7$

Views

Give, Equations,

$\\3x + 2y = 5;\qquad\\ 2x - 3y = 7$

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

$\frac{a_1}{a_2}=\frac{3}{2},\:\frac{b_1}{b_2}=\frac{2}{-3}\:and\:\frac{c_1}{c_2}=\frac{5}{7}$

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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