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