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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 intersect at a point, are parallel or coincident: (i) 5x - 4y + 8 = 0 7x + 6y - 9 = 0

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 intersect at a point, are parallel or coincident:

                    (i)    \\5x - 4y + 8 = 0\\ 7x + 6y - 9 = 0

Answers (1)
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Give, Equations,

\\5x - 4y + 8 = 0\\ 7x + 6y - 9 = 0

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{5}{7},\:\frac{b_1}{b_2}=\frac{-4}{6}\:and\:\frac{c_1}{c_2}=\frac{8}{-9}

As we can see 

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

It means that both lines intersect at exactly one point.

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