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a*x+b*y-82/9=0 la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
a*x + b*y - 82/9 = 0
$$\left(a x + b y\right) - \frac{82}{9} = 0$$
Solución detallada
Tenemos una ecuación lineal:
a*x+b*y-82/9 = 0

Transportamos los términos libres (sin x)
del miembro izquierdo al derecho, obtenemos:
$$a x + b y = \frac{82}{9}$$
Dividamos ambos miembros de la ecuación en (a*x + b*y)/x
x = 82/9 / ((a*x + b*y)/x)

Obtenemos la respuesta: x = (82/9 - b*y)/a
Resolución de la ecuación paramétrica
Se da la ecuación con parámetro:
$$a x + b y - \frac{82}{9} = 0$$
Коэффициент при x равен
$$a$$
entonces son posibles los casos para a :
$$a < 0$$
$$a = 0$$
Consideremos todos los casos con detalles:
Con
$$a < 0$$
la ecuación será
$$b y - x - \frac{82}{9} = 0$$
su solución
$$x = b y - \frac{82}{9}$$
Con
$$a = 0$$
la ecuación será
$$b y - \frac{82}{9} = 0$$
su solución
Gráfica
Suma y producto de raíces [src]
suma
  /  (82/9 - re(b*y))*im(a)    im(b*y)*re(a) \   (82/9 - re(b*y))*re(a)    im(a)*im(b*y) 
I*|- ---------------------- - ---------------| + ---------------------- - ---------------
  |       2        2            2        2   |        2        2            2        2   
  \     im (a) + re (a)       im (a) + re (a)/      im (a) + re (a)       im (a) + re (a)
$$\frac{\left(\frac{82}{9} - \operatorname{re}{\left(b y\right)}\right) \operatorname{re}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} + i \left(- \frac{\left(\frac{82}{9} - \operatorname{re}{\left(b y\right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} - \frac{\operatorname{re}{\left(a\right)} \operatorname{im}{\left(b y\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}\right) - \frac{\operatorname{im}{\left(a\right)} \operatorname{im}{\left(b y\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}$$
=
  /  (82/9 - re(b*y))*im(a)    im(b*y)*re(a) \   (82/9 - re(b*y))*re(a)    im(a)*im(b*y) 
I*|- ---------------------- - ---------------| + ---------------------- - ---------------
  |       2        2            2        2   |        2        2            2        2   
  \     im (a) + re (a)       im (a) + re (a)/      im (a) + re (a)       im (a) + re (a)
$$\frac{\left(\frac{82}{9} - \operatorname{re}{\left(b y\right)}\right) \operatorname{re}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} + i \left(- \frac{\left(\frac{82}{9} - \operatorname{re}{\left(b y\right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} - \frac{\operatorname{re}{\left(a\right)} \operatorname{im}{\left(b y\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}\right) - \frac{\operatorname{im}{\left(a\right)} \operatorname{im}{\left(b y\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}$$
producto
  /  (82/9 - re(b*y))*im(a)    im(b*y)*re(a) \   (82/9 - re(b*y))*re(a)    im(a)*im(b*y) 
I*|- ---------------------- - ---------------| + ---------------------- - ---------------
  |       2        2            2        2   |        2        2            2        2   
  \     im (a) + re (a)       im (a) + re (a)/      im (a) + re (a)       im (a) + re (a)
$$\frac{\left(\frac{82}{9} - \operatorname{re}{\left(b y\right)}\right) \operatorname{re}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} + i \left(- \frac{\left(\frac{82}{9} - \operatorname{re}{\left(b y\right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} - \frac{\operatorname{re}{\left(a\right)} \operatorname{im}{\left(b y\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}\right) - \frac{\operatorname{im}{\left(a\right)} \operatorname{im}{\left(b y\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}$$
=
                 (-82 + 9*re(b*y))*re(a)   I*((-82 + 9*re(b*y))*im(a) - 9*im(b*y)*re(a))
-im(a)*im(b*y) - ----------------------- + ---------------------------------------------
                            9                                    9                      
----------------------------------------------------------------------------------------
                                      2        2                                        
                                    im (a) + re (a)                                     
$$\frac{\frac{i \left(\left(9 \operatorname{re}{\left(b y\right)} - 82\right) \operatorname{im}{\left(a\right)} - 9 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(b y\right)}\right)}{9} - \frac{\left(9 \operatorname{re}{\left(b y\right)} - 82\right) \operatorname{re}{\left(a\right)}}{9} - \operatorname{im}{\left(a\right)} \operatorname{im}{\left(b y\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}$$
(-im(a)*im(b*y) - (-82 + 9*re(b*y))*re(a)/9 + i*((-82 + 9*re(b*y))*im(a) - 9*im(b*y)*re(a))/9)/(im(a)^2 + re(a)^2)
Respuesta rápida [src]
       /  (82/9 - re(b*y))*im(a)    im(b*y)*re(a) \   (82/9 - re(b*y))*re(a)    im(a)*im(b*y) 
x1 = I*|- ---------------------- - ---------------| + ---------------------- - ---------------
       |       2        2            2        2   |        2        2            2        2   
       \     im (a) + re (a)       im (a) + re (a)/      im (a) + re (a)       im (a) + re (a)
$$x_{1} = \frac{\left(\frac{82}{9} - \operatorname{re}{\left(b y\right)}\right) \operatorname{re}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} + i \left(- \frac{\left(\frac{82}{9} - \operatorname{re}{\left(b y\right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} - \frac{\operatorname{re}{\left(a\right)} \operatorname{im}{\left(b y\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}\right) - \frac{\operatorname{im}{\left(a\right)} \operatorname{im}{\left(b y\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}$$
x1 = (82/9 - re(b*y))*re(a)/(re(a)^2 + im(a)^2) + i*(-(82/9 - re(b*y))*im(a)/(re(a)^2 + im(a)^2) - re(a)*im(b*y)/(re(a)^2 + im(a)^2)) - im(a)*im(b*y)/(re(a)^2 + im(a)^2)