Question

if 2x+3y=7 and 3x+2y=3, then the value of x+y is​

Answer 1

SOLUTION:-

Given equation;

⏺️2x+3y=7.......(1)

⏺️3x+2y=3.......(2)

Therefore,

From equation (1), we get;

=) 2x + 3y= 7

=) 2x = 7 -3y

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

Now,

Putting the value of x in eq. (2), we get;

$= > 3( \frac{7 - 3y}{2} ) + 2y = 3 \\ \\ = > \frac{21 - 9y}{2} + 2y = 3 \\ \\ = > 21 - 9y + 4y = 6 \\ \\ = > 21 - 5y = 6 \\ \\ = > - 5y = 6 - 21 \\ \\ = > - 5y = - 15 \\ \\ = > y = \frac{ - 15}{ - 5} \\ \\ = > y = 3$

So,

Eliminate the value of y in eq.(3);

$x = \frac{7 - 3y}{2} \\ \\ = > \frac{7 - 3(3)}{2} \\ \\ = > \frac{7 - 9}{2} \\ \\ = > \frac{ - 2}{2} \\ \\ = > x = - 1$

Thus,

Value of x + y is;

=) -1 + 3

=) 2

Hope it helps ☺️