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Mathematics

Which of the following pairs of linear equations are consistent/inconsistent ? If consistent, obtain the solution graphically :

x - y = 8, 3x - 3y = 16

Linear Equations

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Answer

Given,

Equations :

⇒ x - y = 8, 3x - 3y = 16

⇒ x - y - 8 = 0, 3x - 3y - 16 = 0.

Comparing equations x - y - 8 = 0 and 3x - 3y - 16 = 0 with a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0 respectively, we get :

a1 = 1, b1 = -1, c1 = -8, a2 = 3, b2 = -3 and c2 = -16.

a1a2=13\dfrac{a1}{a2} = \dfrac{1}{3}

b1b2=−1−3=13\dfrac{b1}{b2} = \dfrac{-1}{-3} = \dfrac{1}{3}

c1c2=−8−16=12\dfrac{c1}{c2} = \dfrac{-8}{-16} = \dfrac{1}{2}

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

Hence, pair of lines are inconsistent.

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