X+y=5 and 2x-y=3 simultaneously

Step-by-step explanation:

x + y = 5 - - - (1)

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

adding both the equation

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

=> x + y + 2x - y = 8

=> 3x = 8

=> x = 8/3

by substitution methodsubstitute the value of x in equation (2)

=> 2x - y = 3

=> 2*8/3 - y = 3

=> 16/3 - y = 3

=> 16/3 - 3 = y

=> y = 16 - 9/3

=> y = 7/3

Verification : -

Putting the value of x and y in both the equation

x + y = 5

LHS

=> 8/3 + 7/3

=> 8+7/3

=> 15/3 = 5 = RHS verified

2x - y = 3

(LHS)

__> 2*8/3 - 7/3

and then

__> 16/3 - 7/3

__>16-7/3

__>9/3 = 3 = RHS verified

Adding both equations we get:

3x = 8

x = (8/3) then we solve for y

(8/3) + y = 5

y = 5 - (8/3)

y = (7/3)