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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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