The pair of linear equations 3x + 2y = 5; 2x − 3y = 7 have


The pair of linear equations 3x + 2y = 5; 2x − 3y = 7 have

(a) One solution

(b) Two solutions

(c) Many solutions

(d) No solution


The two equations are

3x + 2y = 5 …… (1)

2x − 3y = 7 …… (2)


$a_{1}=3, b_{1}=2, c_{1}=5$

$a_{2}=2, b_{2}=-3, c_{2}=7$

$\frac{a_{1}}{a_{2}}=\frac{3}{2}, \frac{b_{1}}{b_{2}}=-\frac{2}{3}$

$\therefore \frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}}$

Therefore, they will intersect each other at a unique point and thus, there will be a unique solution for these equations. That is, there is only one solution.

Hence the correct option is 


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