On comparing the ratios `a_1/a_2, b_1/b_2 and c_1/c_2`, find out whether the following pair of linear equations are consistent, or inconsistent.

5x – 3y = 11 ; – 10x + 6y = –22

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#### Solution

5x - 3 y = 11

– 10x + 6y = –22

`a_1/a_2=5/(-10)=(-1)/2, b_1/b_2= (-3)/6 = (-1)/2, c_1/c_2 = 11/-22=(-1)/2`

Since `a_1/a_2=b_1/b_2=c_1/c_2`

Therefore, these linear equations are coincident pair of lines and thus have infinite number of possible solutions. Hence, the pair of linear equations is consistent.

Concept: Graphical Method of Solution of a Pair of Linear Equations

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