If x (x+y) = 27 and y (x+y) = 54, what is the value of (x+y)^2?

9x^2

Step-by-step explanation:

It is given that:

x ( x + y ) = 27

If one manipulates the equation, by dividing by x, they get:

x + y = 27/x

It is also given that:

y ( x + y ) = 54

Again, manipulate the equation, only this time, divide by y,

x + y = 54/y

It is obvious that;

x + y = x + y

Yet this was proven;

x + y = 27/x

x + y = 54/y

Therefore, the following has to be true;

27/x = 54/y

To sove the proportion, use cross products;

27/x = 54/y

54x = 27y

Inverse operations:

54x = 27y

/27     /27

y = 2x

Substitute;

(x + y)

y = 2x

= (x + 2x)

= 3x

Now solve:

(3x)^2

9x^2

solution:

→c= a b , that is product of a and b is possible only when when a is m × n matrix and b is n × p matrix.

that is, number of columns of a= number of rows of b.

so, size of matrix , c= a b is , if a = (m × n)matrix

b= (n × p)matrix

then a b = [ (m × n)matrix] ×[   (n × p)matrix ]

→→c= a b= [m × p ] matrix

→→size of product a b will be equal to = number of rows of a × number of columns of b