Question

observe as seguintes situações e sua representação em linguagem matematica dois numeros x e y são tais 2x y=6 x-y=3

Answer 1

We have two relations

2*x*y = 6 (2 times x times y is equal to six)

x - y = 3 ( the difference between x and y is trhe)

Where whe have two variables, x and y.

To solve this system, the first step is isolation one of the variables in one of the equations, let's isolate x in the second equation.

x - y = 3

x = 3 + y

now we can replace this in the other equation and then solve it for y.

2*x*y = 6

2*(3 + y)*y = 6

6y + 2y^2 = 6

now we have the quadratic equation:

2y^2 + 6y - 6 = 0

the solutions are:

`y = (-6 + -√(6^2 - 4*2*(-6)) )/(2*2) = (-6 +- 9.2)/(4)`

the solutions are:

y = (-6 + 9,2)/4 = 0.8

y = (-6 - 9.2)/4 = -3.8

if y = 0.8, then:

x = 3 + y = 3.8

if y = -3.8

x = 3 + y = 3 - 3.8 = -0.8

so we have two possible solutions:

(-0.8, -3.8) and (3.8, 0.8)