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# Which of the following pairs of linear equations are consistent/inconsistent? If consistent, obtain the solution graphically: (ii) x - y = 8, 3x - 3 y = 16

Q4.    Which of the following pairs of linear equations are consistent/inconsistent? If consistent, obtain the solution graphically:

(ii)    $x - y = 8,\qquad 3x - 3y = 16$

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Given, Equations,

$\\x - y = 8,\qquad\\ 3x - 3y = 16$

Comparing these equations with  $a_1x+b_1y+c_1=0\:and\:a_2x+b_2y+c_2=0$, we get

$\\\frac{a_1}{a_2}=\frac{1}{3},\\\:\frac{b_1}{b_2}=\frac{-1}{-3}=\frac{1}{3}\:and\\\:\frac{c_1}{c_2}=\frac{8}{16}=\frac{1}{2}$

As we can see

$\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq\frac{c_1}{c_2}$

It means the given equations have no solution and thus pair of linear equations is inconsistent.

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