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xy-2x+4y=25 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
x*y - 2*x + 4*y = 25
4y+(xy−2x)=254 y + \left(x y - 2 x\right) = 25
Simplificar
Solución detallada
Tenemos una ecuación lineal:
x*y-2*x+4*y = 25

Sumamos los términos semejantes en el miembro izquierdo de la ecuación:
-2*x + 4*y + x*y = 25

Move the summands with the other variables
del miembro izquierdo al derecho, obtenemos:
xy−2x=25−4yx y - 2 x = 25 - 4 y
Dividamos ambos miembros de la ecuación en (-2*x + x*y)/x
x = 25 - 4*y / ((-2*x + x*y)/x)

Obtenemos la respuesta: x = (25 - 4*y)/(-2 + y)
Resolución de la ecuación paramétrica
Se da la ecuación con parámetro:
xy−2x+4y=25x y - 2 x + 4 y = 25
Коэффициент при x равен
y−2y - 2
entonces son posibles los casos para y :
y<2y < 2
y=2y = 2
Consideremos todos los casos con detalles:
Con
y<2y < 2
la ecuación será
−x−21=0- x - 21 = 0
su solución
x=−21x = -21
Con
y=2y = 2
la ecuación será
−17=0-17 = 0
su solución
no hay soluciones
Gráfica
Suma y producto de raíces [src] 
suma
                                                                   2                                        
  /   (25 - 4*re(y))*im(y)     4*(-2 + re(y))*im(y) \          4*im (y)          (-2 + re(y))*(25 - 4*re(y))
I*|- ---------------------- - ----------------------| - ---------------------- + ---------------------------
  |              2     2                  2     2   |               2     2                     2     2     
  \  (-2 + re(y))  + im (y)   (-2 + re(y))  + im (y)/   (-2 + re(y))  + im (y)      (-2 + re(y))  + im (y)
(25−4re⁡(y))(re⁡(y)−2)(re⁡(y)−2)2+(im⁡(y))2+i(−(25−4re⁡(y))im⁡(y)(re⁡(y)−2)2+(im⁡(y))2−4(re⁡(y)−2)im⁡(y)(re⁡(y)−2)2+(im⁡(y))2)−4(im⁡(y))2(re⁡(y)−2)2+(im⁡(y))2\frac{\left(25 - 4 \operatorname{re}{\left(y\right)}\right) \left(\operatorname{re}{\left(y\right)} - 2\right)}{\left(\operatorname{re}{\left(y\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} + i \left(- \frac{\left(25 - 4 \operatorname{re}{\left(y\right)}\right) \operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{4 \left(\operatorname{re}{\left(y\right)} - 2\right) \operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}}\right) - \frac{4 \left(\operatorname{im}{\left(y\right)}\right)^{2}}{\left(\operatorname{re}{\left(y\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} 
=
                                                                   2                                        
  /   (25 - 4*re(y))*im(y)     4*(-2 + re(y))*im(y) \          4*im (y)          (-2 + re(y))*(25 - 4*re(y))
I*|- ---------------------- - ----------------------| - ---------------------- + ---------------------------
  |              2     2                  2     2   |               2     2                     2     2     
  \  (-2 + re(y))  + im (y)   (-2 + re(y))  + im (y)/   (-2 + re(y))  + im (y)      (-2 + re(y))  + im (y)
(25−4re⁡(y))(re⁡(y)−2)(re⁡(y)−2)2+(im⁡(y))2+i(−(25−4re⁡(y))im⁡(y)(re⁡(y)−2)2+(im⁡(y))2−4(re⁡(y)−2)im⁡(y)(re⁡(y)−2)2+(im⁡(y))2)−4(im⁡(y))2(re⁡(y)−2)2+(im⁡(y))2\frac{\left(25 - 4 \operatorname{re}{\left(y\right)}\right) \left(\operatorname{re}{\left(y\right)} - 2\right)}{\left(\operatorname{re}{\left(y\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} + i \left(- \frac{\left(25 - 4 \operatorname{re}{\left(y\right)}\right) \operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{4 \left(\operatorname{re}{\left(y\right)} - 2\right) \operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}}\right) - \frac{4 \left(\operatorname{im}{\left(y\right)}\right)^{2}}{\left(\operatorname{re}{\left(y\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} 
producto
                                                                   2                                        
  /   (25 - 4*re(y))*im(y)     4*(-2 + re(y))*im(y) \          4*im (y)          (-2 + re(y))*(25 - 4*re(y))
I*|- ---------------------- - ----------------------| - ---------------------- + ---------------------------
  |              2     2                  2     2   |               2     2                     2     2     
  \  (-2 + re(y))  + im (y)   (-2 + re(y))  + im (y)/   (-2 + re(y))  + im (y)      (-2 + re(y))  + im (y)
(25−4re⁡(y))(re⁡(y)−2)(re⁡(y)−2)2+(im⁡(y))2+i(−(25−4re⁡(y))im⁡(y)(re⁡(y)−2)2+(im⁡(y))2−4(re⁡(y)−2)im⁡(y)(re⁡(y)−2)2+(im⁡(y))2)−4(im⁡(y))2(re⁡(y)−2)2+(im⁡(y))2\frac{\left(25 - 4 \operatorname{re}{\left(y\right)}\right) \left(\operatorname{re}{\left(y\right)} - 2\right)}{\left(\operatorname{re}{\left(y\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} + i \left(- \frac{\left(25 - 4 \operatorname{re}{\left(y\right)}\right) \operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{4 \left(\operatorname{re}{\left(y\right)} - 2\right) \operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}}\right) - \frac{4 \left(\operatorname{im}{\left(y\right)}\right)^{2}}{\left(\operatorname{re}{\left(y\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} 
=
 /    2                                               \ 
-\4*im (y) + (-25 + 4*re(y))*(-2 + re(y)) + 17*I*im(y)/ 
--------------------------------------------------------
                             2     2                    
                 (-2 + re(y))  + im (y)
−(re⁡(y)−2)(4re⁡(y)−25)+4(im⁡(y))2+17iim⁡(y)(re⁡(y)−2)2+(im⁡(y))2- \frac{\left(\operatorname{re}{\left(y\right)} - 2\right) \left(4 \operatorname{re}{\left(y\right)} - 25\right) + 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 17 i \operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} 
-(4*im(y)^2 + (-25 + 4*re(y))*(-2 + re(y)) + 17*i*im(y))/((-2 + re(y))^2 + im(y)^2)
Respuesta rápida [src] 
                                                                        2                                        
       /   (25 - 4*re(y))*im(y)     4*(-2 + re(y))*im(y) \          4*im (y)          (-2 + re(y))*(25 - 4*re(y))
x1 = I*|- ---------------------- - ----------------------| - ---------------------- + ---------------------------
       |              2     2                  2     2   |               2     2                     2     2     
       \  (-2 + re(y))  + im (y)   (-2 + re(y))  + im (y)/   (-2 + re(y))  + im (y)      (-2 + re(y))  + im (y)
x1=(25−4re⁡(y))(re⁡(y)−2)(re⁡(y)−2)2+(im⁡(y))2+i(−(25−4re⁡(y))im⁡(y)(re⁡(y)−2)2+(im⁡(y))2−4(re⁡(y)−2)im⁡(y)(re⁡(y)−2)2+(im⁡(y))2)−4(im⁡(y))2(re⁡(y)−2)2+(im⁡(y))2x_{1} = \frac{\left(25 - 4 \operatorname{re}{\left(y\right)}\right) \left(\operatorname{re}{\left(y\right)} - 2\right)}{\left(\operatorname{re}{\left(y\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} + i \left(- \frac{\left(25 - 4 \operatorname{re}{\left(y\right)}\right) \operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{4 \left(\operatorname{re}{\left(y\right)} - 2\right) \operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}}\right) - \frac{4 \left(\operatorname{im}{\left(y\right)}\right)^{2}}{\left(\operatorname{re}{\left(y\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} 
x1 = (25 - 4*re(y))*(re(y) - 2)/((re(y) - 2)^2 + im(y)^2) + i*(-(25 - 4*re(y))*im(y)/((re(y) - 2)^2 + im(y)^2) - 4*(re(y) - 2)*im(y)/((re(y) - 2)^2 + im(y)^2)) - 4*im(y)^2/((re(y) - 2)^2 + im(y)^2)
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