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ax+by+c=0 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
a*x + b*y + c = 0
c+(ax+by)=0c + \left(a x + b y\right) = 0
Simplificar
Solución detallada
Tenemos una ecuación lineal:
a*x+b*y+c = 0

Dividamos ambos miembros de la ecuación en (c + a*x + b*y)/x
x = 0 / ((c + a*x + b*y)/x)

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