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.

3x + 2y = 5 ; 2x – 3y = 7

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#### Solution

3x + 2y = 5

2x - 3y = 7

`a_1/a_2 = 3/2, b_1/b_2 = (-2)/3, (c_1)/(c_2)= 5/7`

`a_1/a_2 != b_1/b_2`

These linear equations are intersecting each other at one point and thus have only one possible solution. Hence, the pair of linear equations is consistent.

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

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