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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

Answers (1)
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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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