System of equatio135ns

Código CM03-E3004-I

VIEW:411 DATA:2020-03-20
Systems of equations are very important, and have several uses. A manager and an attendant were placed in a store, and the cost of staff in that store is 100 monetary units.
In another store we have a manager and three attendants, and the cost of this store with personnel is 150 currency units. What is the ratio of the attendant salary to the manager.
A. The manager receives 3 times the attendant's salary.
B. The manager and attendant have the same salary.
C. The attendant receives 3 times the manager's salary.
D. The manager receives 2 times the attendant's salary.
E. It is not possible to know the salary of the defined positions.

So we can control the wages of groups of individuals in stores, and be able to see ways to save or organize stores, using equation systems. In the case of the question, let's say that the manager's salary is represented by the symbol "x", and the symbol that represents the attendant's salary is "y".
In store one, we have that an "x" plus a "y" is equal to 100. This is the first equation. In the second store we have an "x" plus three "y" that is equal to 150. Now we have both equations as systems of equation.
The first way to solve it is to put the "x" or "y" in evidence. So let's put the "x" in evidence, evidence is trying to isolate the "x". So we have that "x" is equal to 100 minus "y".
Then we replace the "x" in the second, meaning "x" in the first. That way we have 100 minus "y", plus three "y" equal to 150. We can solve, three "y" minus "y" is equal to two "y", and 100 we can put after the equal by changing the sign.
So we have two "y" equal to 150 minus 100, which we have two "y" equal to 50, so we can divide by two, and so we have y is equal to 25, which tells us that the attendant wins 25 currency units . We have that "x" plus "y" is equal to 100, we know that "y" is 25, so we substitute and we have "x" plus 25 equal to 100, so we have x is equal to 75, so we have that the manager receives 75 currency units.
So in a company we can find out how much each position receives, knowing when to spend with the offices. And this is important for managing companies.
Another way to solve, which is in the generalized system, is to try to make us have an identity matrix. Identity matrix is ​​one that each column has a number of 1, and the other values ​​of the line equal to 0, let's do the example to understand.
Looking at the system of equations, we can remove the "x" and "y", and we only have numbers separated by rows and columns. Note that x is in the first column and y in the second column and the quantity in the third column.
So now we have only the numbers. The goal is to make the matrix x and y equal to the identity matrix. Identity matrix is ​​when we have 1 in just one column of a row and other values ​​are zeros, and the other rows are not equal to the first, and have a value of 1 in another column and the other values ​​are zero.
This method is the system used for every computer system. Thus, the computer works in this search to find the answer. We call this Linear Algebra.
To be able to reset the first column of the second row, subtract the bottom row with the top row. See that we use the top line to subtract below.
The value 3 that is in the column of the y, subtracted with the 1 from the top y, giving the value two. But we don't want the two we want the 1, so just divide the whole line by two, and then we have 1 in the y column, which tells us that the y is 25, so knowing that the y is the attendant, then we have the attendant wins 25 currency units.
Now that we have the 1 at the bottom we subtract it at the top, and so the y of the top column is zero, leaving only the 1 of the x column, so we have x is 75, we know that x is the manager, so the manager receives 75 units monetary
See that the answer is that the manager receives three times, which the attendant receives. It can sometimes seem difficult the linear mode, of zeros and one, but knowing the technique and training it always becomes simpler.





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Tags

System of equations, linear algebra, company, salary, mathematics, algebra