Question

if x -y=xy=1-x-y then x +y is 5/6​

Answer 1

Answer:

There are different methods to solve this question, one is given below

As we have given two equations:

x + y = 5 ———(1)

xy = 6 ————(2)

Now find “x” or “y” from equation (1)

x = 5 - y

now put this value in equation (2)

(5 - y )(y) = 6

5y - y^2 = 6

OR

-y^2 + 5y - 6 = 0

Multiplying both sides with “-1”

y^2 - 5y + 6 = 0 ——-(A)

Step-by-step explanation:

so equation (A) becomes;

y^2 - 3y - 2y + 6 = 0

(y^2 - 3y) + (-2y + 6) = 0 ——- (making sets of two numbers having some terms in common)

y(y - 3) -2(y - 3) = 0

taking y-3 common

(y - 3)(y - 2) = 0

using factor theorem we get

y - 3 = 0 & y - 2 = 0

so y = 3/2

Now putting value of y in equation (1)

x + 3 = 5

x = 5–3

x = 2

and

x + 2 = 5

x + 2 = 5

x = 5-2

x = 3

so solution sets are:

(2,3) & (3,2)