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Mathematics

On comparing the ratios a1a2=b1b2=c1c2\dfrac{a1}{a2} = \dfrac{b1}{b2} = \dfrac{c1}{c2} find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincident :

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

Linear Equations

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Answer

Comparing equations 5x - 4y + 8 = 0 and 7x + 6y - 9 = 0 with a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0 respectively, we get :

a1 = 5, b1 = -4, c1 = 8, a2 = 7, b2 = 6 and c2 = -9.

a1a2=57\dfrac{a1}{a2} = \dfrac{5}{7}

b1b2=−46=−23\dfrac{b1}{b2} = \dfrac{-4}{6} = -\dfrac{2}{3}.

Since, a1a2\dfrac{a1}{a2} ≠ b1b2\dfrac{b1}{b2}.

Hence, the set of linear equations intersect at a point.

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