What is the value of (x + y)^2 if 2x + y = 11 and 5x – 2y = –1
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calendarEducator since 2008
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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
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calendarEducator since 2010
write12,551 answers
starTop subjects are Math, Science, and Business
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