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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.

3x + 2y = 5 ; 2x - 3y = 7

Linear Equations

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Answer

Given,

Equations : 3x + 2y = 5 ; 2x - 3y = 7 or,

3x + 2y - 5 = 0 ; 2x - 3y - 7 = 0.

Comparing equations 3x + 2y - 5 = 0 and 2x - 3y - 7 = 0 with a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0 respectively, we get :

a1 = 3, b1 = 2, c1 = -5, a2 = 2, b2 = -3 and c2 = -7.

a1a2=32\dfrac{a1}{a2} = \dfrac{3}{2}

b1b2=2−3=−23\dfrac{b1}{b2} = \dfrac{2}{-3} = -\dfrac{2}{3}

Since, a1a2\dfrac{a1}{a2} ≠ b1b2\dfrac{b1}{b2}.

Hence, the set of linear equations are consistent.

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