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xy−3x+2y=12 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
x*y - 3*x + 2*y = 12
2y+(xy−3x)=122 y + \left(x y - 3 x\right) = 12
Simplificar
Solución detallada
Tenemos una ecuación lineal:
x*y-3*x+2*y = 12

Sumamos los términos semejantes en el miembro izquierdo de la ecuación:
-3*x + 2*y + x*y = 12

Move the summands with the other variables
del miembro izquierdo al derecho, obtenemos:
xy−3x=12−2yx y - 3 x = 12 - 2 y
Dividamos ambos miembros de la ecuación en (-3*x + x*y)/x
x = 12 - 2*y / ((-3*x + x*y)/x)

Obtenemos la respuesta: x = 2*(6 - y)/(-3 + y)
Resolución de la ecuación paramétrica
Se da la ecuación con parámetro:
xy−3x+2y=12x y - 3 x + 2 y = 12
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−8=0- x - 8 = 0
su solución
x=−8x = -8
Con
y=3y = 3
la ecuación será
−6=0-6 = 0
su solución
no hay soluciones
Gráfica
Respuesta rápida [src] 
                                                                        2                                       
       /   2*(-3 + re(y))*im(y)     2*(6 - re(y))*im(y)  \          2*im (y)          2*(-3 + re(y))*(6 - 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=2(6−re⁡(y))(re⁡(y)−3)(re⁡(y)−3)2+(im⁡(y))2+i(−2(6−re⁡(y))im⁡(y)(re⁡(y)−3)2+(im⁡(y))2−2(re⁡(y)−3)im⁡(y)(re⁡(y)−3)2+(im⁡(y))2)−2(im⁡(y))2(re⁡(y)−3)2+(im⁡(y))2x_{1} = \frac{2 \left(6 - \operatorname{re}{\left(y\right)}\right) \left(\operatorname{re}{\left(y\right)} - 3\right)}{\left(\operatorname{re}{\left(y\right)} - 3\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} + i \left(- \frac{2 \left(6 - \operatorname{re}{\left(y\right)}\right) \operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)} - 3\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{2 \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}}\right) - \frac{2 \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 = 2*(6 - re(y))*(re(y) - 3)/((re(y) - 3)^2 + im(y)^2) + i*(-2*(6 - re(y))*im(y)/((re(y) - 3)^2 + im(y)^2) - 2*(re(y) - 3)*im(y)/((re(y) - 3)^2 + im(y)^2)) - 2*im(y)^2/((re(y) - 3)^2 + im(y)^2)
Suma y producto de raíces [src] 
suma
                                                                   2                                       
  /   2*(-3 + re(y))*im(y)     2*(6 - re(y))*im(y)  \          2*im (y)          2*(-3 + re(y))*(6 - 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)
2(6−re⁡(y))(re⁡(y)−3)(re⁡(y)−3)2+(im⁡(y))2+i(−2(6−re⁡(y))im⁡(y)(re⁡(y)−3)2+(im⁡(y))2−2(re⁡(y)−3)im⁡(y)(re⁡(y)−3)2+(im⁡(y))2)−2(im⁡(y))2(re⁡(y)−3)2+(im⁡(y))2\frac{2 \left(6 - \operatorname{re}{\left(y\right)}\right) \left(\operatorname{re}{\left(y\right)} - 3\right)}{\left(\operatorname{re}{\left(y\right)} - 3\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} + i \left(- \frac{2 \left(6 - \operatorname{re}{\left(y\right)}\right) \operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)} - 3\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{2 \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}}\right) - \frac{2 \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                                       
  /   2*(-3 + re(y))*im(y)     2*(6 - re(y))*im(y)  \          2*im (y)          2*(-3 + re(y))*(6 - 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)
2(6−re⁡(y))(re⁡(y)−3)(re⁡(y)−3)2+(im⁡(y))2+i(−2(6−re⁡(y))im⁡(y)(re⁡(y)−3)2+(im⁡(y))2−2(re⁡(y)−3)im⁡(y)(re⁡(y)−3)2+(im⁡(y))2)−2(im⁡(y))2(re⁡(y)−3)2+(im⁡(y))2\frac{2 \left(6 - \operatorname{re}{\left(y\right)}\right) \left(\operatorname{re}{\left(y\right)} - 3\right)}{\left(\operatorname{re}{\left(y\right)} - 3\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} + i \left(- \frac{2 \left(6 - \operatorname{re}{\left(y\right)}\right) \operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)} - 3\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{2 \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}}\right) - \frac{2 \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                                       
  /   2*(-3 + re(y))*im(y)     2*(6 - re(y))*im(y)  \          2*im (y)          2*(-3 + re(y))*(6 - 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)
2(6−re⁡(y))(re⁡(y)−3)(re⁡(y)−3)2+(im⁡(y))2+i(−2(6−re⁡(y))im⁡(y)(re⁡(y)−3)2+(im⁡(y))2−2(re⁡(y)−3)im⁡(y)(re⁡(y)−3)2+(im⁡(y))2)−2(im⁡(y))2(re⁡(y)−3)2+(im⁡(y))2\frac{2 \left(6 - \operatorname{re}{\left(y\right)}\right) \left(\operatorname{re}{\left(y\right)} - 3\right)}{\left(\operatorname{re}{\left(y\right)} - 3\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} + i \left(- \frac{2 \left(6 - \operatorname{re}{\left(y\right)}\right) \operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)} - 3\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{2 \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}}\right) - \frac{2 \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                                             \ 
-\2*im (y) + 2*(-6 + re(y))*(-3 + re(y)) + 6*I*im(y)/ 
------------------------------------------------------
                            2     2                   
                (-3 + re(y))  + im (y)
−2(re⁡(y)−6)(re⁡(y)−3)+2(im⁡(y))2+6iim⁡(y)(re⁡(y)−3)2+(im⁡(y))2- \frac{2 \left(\operatorname{re}{\left(y\right)} - 6\right) \left(\operatorname{re}{\left(y\right)} - 3\right) + 2 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 6 i \operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)} - 3\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} 
-(2*im(y)^2 + 2*(-6 + re(y))*(-3 + re(y)) + 6*i*im(y))/((-3 + re(y))^2 + im(y)^2)
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