Question

Find the number of solutions for the pair of linear equations 3x+2y = 5 ; 2x-3y = 7.

Answer 1

$\huge\mathcal{Answer:}$

$3x + 2y = 5 - - (1)$

$2x - 3y = 7 - - (2)$

Multiply (1) by (2)

$6x + 4y = 10 - - (3)$

$6x - 9y = 21 - - (4)$

subtract eq (3) by (4)

$13y = - 11$

$y = - \frac{11}{3}$

substitute the value of y in (1)

$3x + 2( - \frac{11}{13} ) = 5$

$3x - \frac{22}{13} = 5$

$3x = \frac{87}{13}$

$x = \frac{29}{13}$

$x = \frac{29}{3} y = \frac{ - 11}{13}$

Answer 2

Answer:

3x + 2y = 5 - - (1)

2x - 3y = 7 - - (2)

Multiply (1) by (2)

6x + 4y = 10 - - (3)

6x - 9y = 21 - - (4)

subtract eq (3) by (4)

13y = - 1113y=−11

$y = - \frac{11}{3}$

substitute the value of y in (1)

$3x + 2( - \frac{11}{13} ) = 5$

$3x - \frac{22}{13} = 5$

$3x = \frac{87}{13}$

$x = \frac{29}{13}$

$x = \frac{29}{3} y = \frac{ - 11}{13}$