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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 :

6x - 3y + 10 = 0 and 2x - y + 9 = 0

Linear Equations

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Answer

Comparing equations 6x - 3y + 10 = 0 and 2x - y + 9 = 0 with a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0 respectively, we get :

a1 = 6, b1 = -3, c1 = 10, a2 = 2, b2 = -1 and c2 = 9.

a1a2=62=3\dfrac{a1}{a2} = \dfrac{6}{2} = 3

b1b2=−3−1=3\dfrac{b1}{b2} = \dfrac{-3}{-1} = 3

c1c2=109\dfrac{c1}{c2} = \dfrac{10}{9}

Since, a1a2\dfrac{a1}{a2} = b1b2\dfrac{b1}{b2} ≠ c1c2\dfrac{c1}{c2}.

Hence, the set of linear equations are parallel.

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