Question

If 3x + 5y = 9 and 5x + 3y = 7 then What is the value of x +y =?​

Answer 1

Answer is 2

Sol. 3x + 5y = 9
5x + 3y = 7
——————-
Add. 8x + 8y = 16

8(x+y) = 16
x+y = 16/8
x+ y = 2

Answer 2

$3x + 5y = 9...........(1) \\ 5x + 3y = 7..........(2) \\ 1) \times 5 = 15x + 25y = 45 \\ 2) \times 3 = 15x + 9y = 21$

To cancel,we have to subtract the equation,so that we have to change the sign

$15x + 25y = 45 \\ - 15x - 9y = - 21 \\ 16y = 24 \\ y = \frac{24}{16} \\ y = \frac{3}{2} \\ sub \: y = \frac{3}{2} \: in \: equation \: 1. \\ 3x + 5y = 9 \\ 3x + 5( \frac{3}{2} ) = 9 \\ 3x + \frac{15}{2} = 9 \\ \frac{6x + 15}{2} = 9 \\ 6x + 15 = 18 \\ 6x = 18 - 15 \\ 6x = 3 \\ x = \frac{1}{2}$

Therefore,

$x = \frac{1}{2} \: y = \frac{3}{2}$

X + y = 1/2+3/2=4/2=2

X + y = 2

Hope this will be helpful.