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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 :

9x + 3y + 12 = 0 and 18x + 6y + 24 = 0

Linear Equations

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Answer

Comparing equations 9x + 3y + 12 = 0 and 18x + 6y + 24 = 0 with a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0 respectively, we get :

a1 = 9, b1 = 3, c1 = 12, a2 = 18, b2 = 6 and c2 = 24.

a1a2=918=12\dfrac{a1}{a2} = \dfrac{9}{18} = \dfrac{1}{2}

b1b2=36=12\dfrac{b1}{b2} = \dfrac{3}{6} = \dfrac{1}{2}

c1c2=1224=12\dfrac{c1}{c2} = \dfrac{12}{24} = \dfrac{1}{2}

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

Hence, the set of linear equations are coincident.

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