Respuesta :

Answer:

x+y = 14

Step-by-step explanation:

x+y+xy = 54

1+x+y+xy = 55

(1+x)(1+y) = 55

(1+x)(1+y) = 5*11

If x and y are integers,

1+x = 5    => x = 4

1+y = 11   =>  y = 10

or

1+x = 11   => x = 10

1+y = 5   =>  y = 4

In either case, x+y = 14

The solution to this system is [tex]x = 4[/tex] and [tex]y = 10[/tex]. Then, [tex]x+y = 14[/tex].

Let be [tex]x + y + x\cdot y = 54[/tex], then we proceed to modify the expression by algebraic means:

  1. [tex]x + y + x\cdot y = 54[/tex]  Given
  2. [tex]x+y+x\cdot y + 1 = 55[/tex]  Compatibility with addition/Definition of addition
  3. [tex](x+1)+(y+x\cdot y) = 55[/tex]  Commutative property/Associative property
  4. [tex](x+1) + y\cdot (x + 1) = 55[/tex]  Distributive property/Commutative property
  5. [tex](x+1)\cdot (y +1) = 55[/tex]  Distributive property

The only divisors of 55 is 5 and 11, respectively. Hence, we have the following  system of linear equations:

[tex]x + 1 = 5[/tex] (1)

[tex]y + 1 = 11[/tex] (2)

The solution to this system is [tex]x = 4[/tex] and [tex]y = 10[/tex]. Then, [tex]x+y = 14[/tex].

To learn more on integers, we kindly invite to check this verified question: https://brainly.com/question/1768254

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