The system of the equations represents set of mathematical records, each of which contains a number of variables. There are several ways of their decision.
It is required to you
- - ruler and pencil;
- - calculator.
Instruction
1. To solve the system of the equations - means to find a set of all its solutions, or to prove that it has no them. It can be written down by means of the brace.
2. For the solution of a system of the equations with two variables usually use the following methods: graphic way, way of substitution and way of addition. Let's dwell upon the first of above-mentioned options.
3. Let's consider the sequence of the solution of a system which consists of the linear equations having an appearance: a1x + b1y = c1 and a2x + b2y = c2. Where x and y – unknown variables, and b, c – free members. At application of this way each solution of a system represents coordinates of points of the straight lines corresponding to each equation. For a start in each case express one variable through another. Then set a variable x several any values. Substitute enough two in the equation and find y. Construct the system of coordinates, note on it the received points and draw through them a straight line. Similar calculations need to be carried out also for other parts of a system.
4. The point or points of intersection of the constructed schedules will also be the solution of this set of the equations.
5. The system has the only decision if the constructed straight lines are crossed and have one general point. It is a nesovmestna if schedules are parallel each other. Also has infinitely many decisions when straight lines merge with each other.
6. This way is considered very evident. The main shortcoming is that the found unknown have approximate values. More exact result is yielded by so-called algebraic methods.
7. Any solution of a system of the equations should be checked. For this purpose substitute the received values instead of variables. It is also possible to find its solution by several methods. If the solution of a system true, then all answers have to turn out identical.