The equation call analytical record of a task about investigation of values of arguments at which values of two these functions are equal. The system is a set of the equations for which it is required to find values of the unknown satisfying at the same time to all these equations. As the successful solution of a task is impossible without correctly made system of the equations, it is necessary to know the basic principles of drawing up similar systems.
Instruction
1. First, determine unknown sizes which are required to be found in this task. Designate them through variables. The most widespread variables used at the solution of systems of the equations, it x, y and z. In separate tasks it is more convenient to apply the standard designations, for example, V to designation of volume, or a for acceleration designation.
2. Example. Let the hypotenuse of a rectangular triangle be equal to 5 m. It is necessary to define legs if it is known that after to increase one of them by 3 times, and another in 4, then the sum of their lengths will be 29 m. For this task it is necessary to designate lengths of legs through variables x and y.
3. Further attentively read a statement of the problem and connect unknown sizes by the equations. Sometimes the interrelation between variables will be obvious. For example, in the example given above, legs are connected by the following ratio. If "to increase one of them by 3 times" (3 * x), "and another in 4" (4 * y), "that the sum of their lengths will be 29 m": 3 * x + 4 * y = 29.
4. Other equation is less obvious to this task. It is in a condition to a task that the rectangular triangle is given. Means, it is possible to apply Pythagorean theorem. I.e. x^2 + y^2 = 25. Total two equations turn out: 3 * x + 4 * y = 29 and x^2 + y^2 = 25. In order that the system had the unambiguous decision, the quantity of the equations has to be equal to the number of unknown. In the given example there are two variable also two equations. Means, the system has one concrete decision: x = 3 m, y = 4 m.
5. At the solution of physical tasks the "unobvious" equations can consist in the formulas connecting physical quantities. For example, let it is necessary to find speeds of pedestrians of Va and Vb in a statement of the problem. It is known that the pedestrian of A passes S distance for 3 hours more slowly, than the pedestrian of B. Then it is possible to work out the equation, having used formula S = V * t where S is a distance, V – the speed, t – time: S / Va = S/Vb + 3. Here S/Va is time for which there will pass the set distance a pedestrian of A. S / Vb - time for which there will pass the set distance a pedestrian of B. On a condition this time is 3 watch less.