Mister Exam

Lang:

0,3x+0,03y=0,12(x+y) equation

The teacher will be very surprised to see your correct solution 😉

You have entered [src]

3*x   3*y   3*(x + y)
--- + --- = ---------
 10   100       25

\frac{3 x}{10} + \frac{3 y}{100} = \frac{3 \left(x + y\right)}{25}

Simplify

Detail solution

Given the linear equation:

(3/10)*x+(3/100)*y = (3/25)*(x+y)

Expand brackets in the left part

3/10x+3/100y = (3/25)*(x+y)

Expand brackets in the right part

3/10x+3/100y = 3/25x+y

Looking for similar summands in the left part:

3*x/10 + 3*y/100 = 3/25x+y

Looking for similar summands in the right part:

3*x/10 + 3*y/100 = 3*x/25 + 3*y/25

Move the summands with the other variables
from left part to right part, we given:

\frac{3 x}{10} = \frac{3 x}{25} + \frac{9 y}{100}

Move the summands with the unknown x
from the right part to the left part:

\frac{9 x}{50} = \frac{9 y}{100}

Divide both parts of the equation by 9/50

x = 9*y/100 / (9/50)

We get the answer: x = y/2

The graph

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

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