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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.

2x - 3y = 8 ; 4x - 6y = 9

Linear Equations

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Answer

Given,

Equations : 2x - 3y = 8 ; 4x - 6y = 9 or,

2x - 3y - 8 = 0 ; 4x - 6y - 9 = 0.

Comparing equations 2x - 3y - 8 = 0 and 4x - 6y - 9 = 0 with a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0 respectively, we get :

a1 = 2, b1 = -3, c1 = -8, a2 = 4, b2 = -6 and c2 = -9.

a1a2=24=12\dfrac{a1}{a2} = \dfrac{2}{4} = \dfrac{1}{2}

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

c1c2=−8−9=89\dfrac{c1}{c2} = \dfrac{-8}{-9} = \dfrac{8}{9}

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

Hence, the set of linear equations are inconsistent.

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