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Check whether the number of solutions of 2x + 3y = 12 and 3x + 2y = 13 are Infinity or not. Give reasons.

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The number of solutions to the pair of linear equations a1x + b1y + c1 = 0 a2x + b2y + c2 = 0 are infinity if and only if \(\frac{a_!}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}\)

Here in this case the given pair of linear equations are 

2x + 3y = 12 and 3x + 2y = 13

Hence they will not have infinite solutions.

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