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xy-3x-7y=39 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
x*y - 3*x - 7*y = 39
−7y+(xy−3x)=39- 7 y + \left(x y - 3 x\right) = 39
Simplificar
Solución detallada
Tenemos una ecuación lineal:
x*y-3*x-7*y = 39

Sumamos los términos semejantes en el miembro izquierdo de la ecuación:
-7*y - 3*x + x*y = 39

Move the summands with the other variables
del miembro izquierdo al derecho, obtenemos:
xy−3x=7y+39x y - 3 x = 7 y + 39
Dividamos ambos miembros de la ecuación en (-3*x + x*y)/x
x = 39 + 7*y / ((-3*x + x*y)/x)

Obtenemos la respuesta: x = (39 + 7*y)/(-3 + y)
Resolución de la ecuación paramétrica
Se da la ecuación con parámetro:
xy−3x−7y=39x y - 3 x - 7 y = 39
Коэффициент при x равен
y−3y - 3
entonces son posibles los casos para y :
y<3y < 3
y=3y = 3
Consideremos todos los casos con detalles:
Con
y<3y < 3
la ecuación será
−x−53=0- x - 53 = 0
su solución
x=−53x = -53
Con
y=3y = 3
la ecuación será
−60=0-60 = 0
su solución
no hay soluciones
Gráfica
Suma y producto de raíces [src] 
suma
                                                                   2                                        
  /   (39 + 7*re(y))*im(y)     7*(-3 + re(y))*im(y) \          7*im (y)          (-3 + re(y))*(39 + 7*re(y))
I*|- ---------------------- + ----------------------| + ---------------------- + ---------------------------
  |              2     2                  2     2   |               2     2                     2     2     
  \  (-3 + re(y))  + im (y)   (-3 + re(y))  + im (y)/   (-3 + re(y))  + im (y)      (-3 + re(y))  + im (y)
i(7(re⁡(y)−3)im⁡(y)(re⁡(y)−3)2+(im⁡(y))2−(7re⁡(y)+39)im⁡(y)(re⁡(y)−3)2+(im⁡(y))2)+(re⁡(y)−3)(7re⁡(y)+39)(re⁡(y)−3)2+(im⁡(y))2+7(im⁡(y))2(re⁡(y)−3)2+(im⁡(y))2i \left(\frac{7 \left(\operatorname{re}{\left(y\right)} - 3\right) \operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)} - 3\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{\left(7 \operatorname{re}{\left(y\right)} + 39\right) \operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)} - 3\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}}\right) + \frac{\left(\operatorname{re}{\left(y\right)} - 3\right) \left(7 \operatorname{re}{\left(y\right)} + 39\right)}{\left(\operatorname{re}{\left(y\right)} - 3\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{7 \left(\operatorname{im}{\left(y\right)}\right)^{2}}{\left(\operatorname{re}{\left(y\right)} - 3\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} 
=
                                                                   2                                        
  /   (39 + 7*re(y))*im(y)     7*(-3 + re(y))*im(y) \          7*im (y)          (-3 + re(y))*(39 + 7*re(y))
I*|- ---------------------- + ----------------------| + ---------------------- + ---------------------------
  |              2     2                  2     2   |               2     2                     2     2     
  \  (-3 + re(y))  + im (y)   (-3 + re(y))  + im (y)/   (-3 + re(y))  + im (y)      (-3 + re(y))  + im (y)
i(7(re⁡(y)−3)im⁡(y)(re⁡(y)−3)2+(im⁡(y))2−(7re⁡(y)+39)im⁡(y)(re⁡(y)−3)2+(im⁡(y))2)+(re⁡(y)−3)(7re⁡(y)+39)(re⁡(y)−3)2+(im⁡(y))2+7(im⁡(y))2(re⁡(y)−3)2+(im⁡(y))2i \left(\frac{7 \left(\operatorname{re}{\left(y\right)} - 3\right) \operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)} - 3\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{\left(7 \operatorname{re}{\left(y\right)} + 39\right) \operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)} - 3\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}}\right) + \frac{\left(\operatorname{re}{\left(y\right)} - 3\right) \left(7 \operatorname{re}{\left(y\right)} + 39\right)}{\left(\operatorname{re}{\left(y\right)} - 3\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{7 \left(\operatorname{im}{\left(y\right)}\right)^{2}}{\left(\operatorname{re}{\left(y\right)} - 3\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} 
producto
                                                                   2                                        
  /   (39 + 7*re(y))*im(y)     7*(-3 + re(y))*im(y) \          7*im (y)          (-3 + re(y))*(39 + 7*re(y))
I*|- ---------------------- + ----------------------| + ---------------------- + ---------------------------
  |              2     2                  2     2   |               2     2                     2     2     
  \  (-3 + re(y))  + im (y)   (-3 + re(y))  + im (y)/   (-3 + re(y))  + im (y)      (-3 + re(y))  + im (y)
i(7(re⁡(y)−3)im⁡(y)(re⁡(y)−3)2+(im⁡(y))2−(7re⁡(y)+39)im⁡(y)(re⁡(y)−3)2+(im⁡(y))2)+(re⁡(y)−3)(7re⁡(y)+39)(re⁡(y)−3)2+(im⁡(y))2+7(im⁡(y))2(re⁡(y)−3)2+(im⁡(y))2i \left(\frac{7 \left(\operatorname{re}{\left(y\right)} - 3\right) \operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)} - 3\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{\left(7 \operatorname{re}{\left(y\right)} + 39\right) \operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)} - 3\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}}\right) + \frac{\left(\operatorname{re}{\left(y\right)} - 3\right) \left(7 \operatorname{re}{\left(y\right)} + 39\right)}{\left(\operatorname{re}{\left(y\right)} - 3\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{7 \left(\operatorname{im}{\left(y\right)}\right)^{2}}{\left(\operatorname{re}{\left(y\right)} - 3\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} 
=
    2                                              
7*im (y) + (-3 + re(y))*(39 + 7*re(y)) - 60*I*im(y)
---------------------------------------------------
                           2     2                 
               (-3 + re(y))  + im (y)
(re⁡(y)−3)(7re⁡(y)+39)+7(im⁡(y))2−60iim⁡(y)(re⁡(y)−3)2+(im⁡(y))2\frac{\left(\operatorname{re}{\left(y\right)} - 3\right) \left(7 \operatorname{re}{\left(y\right)} + 39\right) + 7 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 60 i \operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)} - 3\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} 
(7*im(y)^2 + (-3 + re(y))*(39 + 7*re(y)) - 60*i*im(y))/((-3 + re(y))^2 + im(y)^2)
Respuesta rápida [src] 
                                                                        2                                        
       /   (39 + 7*re(y))*im(y)     7*(-3 + re(y))*im(y) \          7*im (y)          (-3 + re(y))*(39 + 7*re(y))
x1 = I*|- ---------------------- + ----------------------| + ---------------------- + ---------------------------
       |              2     2                  2     2   |               2     2                     2     2     
       \  (-3 + re(y))  + im (y)   (-3 + re(y))  + im (y)/   (-3 + re(y))  + im (y)      (-3 + re(y))  + im (y)
x1=i(7(re⁡(y)−3)im⁡(y)(re⁡(y)−3)2+(im⁡(y))2−(7re⁡(y)+39)im⁡(y)(re⁡(y)−3)2+(im⁡(y))2)+(re⁡(y)−3)(7re⁡(y)+39)(re⁡(y)−3)2+(im⁡(y))2+7(im⁡(y))2(re⁡(y)−3)2+(im⁡(y))2x_{1} = i \left(\frac{7 \left(\operatorname{re}{\left(y\right)} - 3\right) \operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)} - 3\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{\left(7 \operatorname{re}{\left(y\right)} + 39\right) \operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)} - 3\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}}\right) + \frac{\left(\operatorname{re}{\left(y\right)} - 3\right) \left(7 \operatorname{re}{\left(y\right)} + 39\right)}{\left(\operatorname{re}{\left(y\right)} - 3\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{7 \left(\operatorname{im}{\left(y\right)}\right)^{2}}{\left(\operatorname{re}{\left(y\right)} - 3\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} 
x1 = i*(7*(re(y) - 3)*im(y)/((re(y) - 3)^2 + im(y)^2) - (7*re(y) + 39)*im(y)/((re(y) - 3)^2 + im(y)^2)) + (re(y) - 3)*(7*re(y) + 39)/((re(y) - 3)^2 + im(y)^2) + 7*im(y)^2/((re(y) - 3)^2 + im(y)^2)
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