What is the value of (x + y)^2 if 2x + y = 11 and 5x – 2y = –1

2x + y = 11.........(1)

5x -
2y = -1..........(2)

We need to find the value of
(x+y)^2

First we will solve the system and determine the
values of x and y.

Multiply (1) by 2 and add to
(2).

==> 4x + 2y =
22

==> 5x - 2y =
-1

==> 9x =
21

==> x = 21/9 =
7/3

==?> y= 11-2x = 11-2*7/3 = 11- 14/3 =
19/3

Then the value is x= 7/3 and y=
19/3

Now we will calculate (x+y)
^2

==> (x+y)^2 = ( 7/3 + 19/3)^2 = (26/3)^2 =
676/9

Then the answer is: (x+y)^2 =
676/9