# If (x^2 - y^2) = 10 and (x + y) = 2, find x and y. We have to solve the equation:

(x^2 - y^2) = 10...(1)

(x + y) = 2...(2)

We know that (x + y)^2 = x^2 + y^2 + 2xy

(2)

=> x + y = 2

=> (x + y)^2 = 4

=> x^2 + y^2 + 2xy = 4

Also...

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We have to solve the equation:

(x^2 - y^2) = 10...(1)

(x + y) = 2...(2)

We know that (x + y)^2 = x^2 + y^2 + 2xy

(2)

=> x + y = 2

=> (x + y)^2 = 4

=> x^2 + y^2 + 2xy = 4

Also from (1)

(x^2 - y^2) = 10

So we have x^2 + y^2 + 2xy - x^2 + y^2 = 4 - 10

=> 2y^2 + 2xy = -6

=> 2y(x+y) = -6

=> 2y(2) = -6

=> y = -3/2

x + y = 2

=> x - 3/2 = 2

=> x = 2 + 3/2

=> x = 7/2

Therefore x = 7/2 and y = -3/2

Approved by eNotes Editorial Team Given that:

x^2 - y^2 = 10..............(1)

x+y = 2..............(2)

We need to find the values of x and y.

First , we will rewrite equation (1)

We know that (x^2 - y^2) = (x-y)(x+y)

==> (x-y)(x+y) = 10

But from (2) we know that (x+y) = 2

==> 2 (x-y) = 10

==> x- y = 5................(3)

Now we will solve the system (2) and (3).

We will add (2) and (3).

==> 2x = 7

==> x = 7/2

==> y= 2- x = 2- 7/2 = -3/2

==> y= -3/2

Then the answer is :

x = 7/2 and y = -3/2

Approved by eNotes Editorial Team