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.

2x – 3y = 8 ; 4x – 6y = 9

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#### Solution

2x - 3y = 8

4x - 6y = 9

`a_1/a_2=2/4=1/2, b_1/b_2=(-3)/-6=1/2, c_1/c_2=8/9`

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

Since

Therefore, these linear equations are parallel to each other and thus have no possible solution.

Hence, the pair of linear equations is inconsistent.

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

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