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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 following pair of linear equations are consistent, or inconsistent.

5x - 3y = 11 ; -10x + 6y = -22

Linear Equations

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Answer

Given,

Equations : 5x - 3y = 11 ; -10x + 6y = -22 or,

5x - 3y - 11 = 0 ; -10x + 6y + 22 = 0

Comparing equations 5x - 3y - 11 = 0 and -10x + 6y + 22 = 0 with a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0 respectively, we get :

a1 = 5, b1 = -3, c1 = -11, a2 = -10, b2 = 6 and c2 = 22.

a1a2=5−10=−12\dfrac{a1}{a2} = \dfrac{5}{-10} = -\dfrac{1}{2}

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

c1c2=−1122=−12\dfrac{c1}{c2} = \dfrac{-11}{22} = -\dfrac{1}{2}

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

Hence, the set of linear equations are consistent.

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