10x+12x+y-12y=0 equation

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You have entered [src]

10*x + 12*x + y - 12*y = 0

$$- 12 y + \left(y + \left(10 x + 12 x\right)\right) = 0$$

Simplify

Detail solution

Given the linear equation:

10*x+12*x+y-12*y = 0

Looking for similar summands in the left part:

-11*y + 22*x = 0

Move the summands with the other variables
from left part to right part, we given:
$$22 x = 11 y$$
Divide both parts of the equation by 22

x = 11*y / (22)

We get the answer: x = y/2

The graph

Rapid solution [src]

     re(y)   I*im(y)
x1 = ----- + -------
       2        2

$$x_{1} = \frac{\operatorname{re}{\left(y\right)}}{2} + \frac{i \operatorname{im}{\left(y\right)}}{2}$$

x1 = re(y)/2 + i*im(y)/2

Sum and product of roots [src]

sum

re(y)   I*im(y)
----- + -------
  2        2

$$\frac{\operatorname{re}{\left(y\right)}}{2} + \frac{i \operatorname{im}{\left(y\right)}}{2}$$

re(y)   I*im(y)
----- + -------
  2        2

$$\frac{\operatorname{re}{\left(y\right)}}{2} + \frac{i \operatorname{im}{\left(y\right)}}{2}$$

product

re(y)   I*im(y)
----- + -------
  2        2

$$\frac{\operatorname{re}{\left(y\right)}}{2} + \frac{i \operatorname{im}{\left(y\right)}}{2}$$

re(y)   I*im(y)
----- + -------
  2        2

$$\frac{\operatorname{re}{\left(y\right)}}{2} + \frac{i \operatorname{im}{\left(y\right)}}{2}$$

re(y)/2 + i*im(y)/2