xy+48y=10,2 equation

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x*y + 48*y = 51/5

$$x y + 48 y = \frac{51}{5}$$

Simplify

Detail solution

Given the linear equation:

x*y+48*y = (51/5)

Expand brackets in the right part

x*y+48*y = 51/5

Divide both parts of the equation by (48*y + x*y)/x

x = 51/5 / ((48*y + x*y)/x)

We get the answer: x = -48 + 51/(5*y)

The solution of the parametric equation

Given the equation with a parameter:
$$x y + 48 y = \frac{51}{5}$$
Коэффициент при x равен
$$y$$
then possible cases for y :
$$y < 0$$
$$y = 0$$
Consider all cases in more detail:
With
$$y < 0$$
the equation
$$- x - \frac{291}{5} = 0$$
its solution
$$x = - \frac{291}{5}$$
With
$$y = 0$$
the equation
$$- \frac{51}{5} = 0$$
its solution
no solutions

The graph

Sum and product of roots [src]

sum

            51*re(y)             51*I*im(y)    
-48 + ------------------- - -------------------
        /  2        2   \     /  2        2   \
      5*\im (y) + re (y)/   5*\im (y) + re (y)/

$$-48 + \frac{51 \operatorname{re}{\left(y\right)}}{5 \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)} - \frac{51 i \operatorname{im}{\left(y\right)}}{5 \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)}$$

            51*re(y)             51*I*im(y)    
-48 + ------------------- - -------------------
        /  2        2   \     /  2        2   \
      5*\im (y) + re (y)/   5*\im (y) + re (y)/

$$-48 + \frac{51 \operatorname{re}{\left(y\right)}}{5 \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)} - \frac{51 i \operatorname{im}{\left(y\right)}}{5 \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)}$$

product

            51*re(y)             51*I*im(y)    
-48 + ------------------- - -------------------
        /  2        2   \     /  2        2   \
      5*\im (y) + re (y)/   5*\im (y) + re (y)/

$$-48 + \frac{51 \operatorname{re}{\left(y\right)}}{5 \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)} - \frac{51 i \operatorname{im}{\left(y\right)}}{5 \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)}$$

  /       2           2                           \
3*\- 80*im (y) - 80*re (y) + 17*re(y) - 17*I*im(y)/
---------------------------------------------------
                  /  2        2   \                
                5*\im (y) + re (y)/

$$\frac{3 \left(- 80 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 17 \operatorname{re}{\left(y\right)} - 80 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 17 i \operatorname{im}{\left(y\right)}\right)}{5 \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)}$$

3*(-80*im(y)^2 - 80*re(y)^2 + 17*re(y) - 17*i*im(y))/(5*(im(y)^2 + re(y)^2))

Rapid solution [src]

                 51*re(y)             51*I*im(y)    
x1 = -48 + ------------------- - -------------------
             /  2        2   \     /  2        2   \
           5*\im (y) + re (y)/   5*\im (y) + re (y)/

$$x_{1} = -48 + \frac{51 \operatorname{re}{\left(y\right)}}{5 \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)} - \frac{51 i \operatorname{im}{\left(y\right)}}{5 \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)}$$

x1 = -48 + 51*re(y)/(5*(re(y)^2 + im(y)^2)) - 51*i*im(y)/(5*(re(y)^2 + im(y)^2))

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xy+48y=10,2 equation

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