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

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

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

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

We have to find the value of (x + y)^2 given the equations 2x + y = 11 and 5x – 2y = –1.

2x + y = 11

=> 2x  = 11 – y

=> x = 11/2 – y/2

Substitute in 5x – 2y = -1

=> 5*(11/2  - y/2) – 2y = -1

=> 55 – 5y – 4y = -2

=> -9y = -57

=> y = 57/9

=> y = 19/3

x = 11/2 – 19/6

=> (33 - 19)/6

=> x = 14/6

=> x = 7/3

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

=> 676/9

The required value of (x + y)^2 = 676/9