The solution of a system of the equations is difficult and fascinating. The system is more difficult, the it is more interesting to solve it. Most often in mathematics of high school the systems of the equations meet two unknown, but in the higher mathematics of variables maybe more. It is possible to solve systems by several methods.
Instruction
1. The most widespread method of the solution of a system of the equations is a substitution. For this purpose it is necessary to express one variable through another and to substitute it in the second equation of a system, thus having led the equation to one variable. For example, the system of the equations is given: 2kh-3u-1=0; x + at-3=0.
2. From the second expression it is convenient to express one of variables, having transferred all the rest to the right part of expression, without having forgotten to replace the sign of coefficient at the same time: x to the =3rd.
3. We substitute this value in the first expression, thus getting rid from x: 2 * (3rd)-3u-1=0.
4. We remove the brackets: 6-2u-3u-1=0; - 5u +5=0; at =1. At we substitute the received value in expression: x to the =3rd; x =3-1; x =2.
5. Removal of the general multiplier and division into it can become in the good way to simplify the system of the equations. For example, the system is given: 4kh-2u-6=0;3х +2u-8=0.
6. In the first expression all members are multiple 2, it is possible to take out 2 for a bracket thanks to distributive property of multiplication: 2 * (2kh-at-3) =0. Now both parts of expression can be reduced by this number, and then to express at as the coefficient on the module at it is equal to unit: - at =3-2kh or at =2kh-3.
7. As well as in the first case, we substitute this expression in the second equation and we receive: the 3rd +2 * (2kh-3)-8=0;3kh +4kh-6-8=0;7kh-14=0;7Õ =14; x =2. We substitute the received value in expression: at =2kh-3; at =4-3=1.
8. But this system of the equations can be solved and it is much simpler - method of subtraction or addition. To receive the simplified expression, it is necessary to subtract term by term from one equation another or to put them. 4kh-2u-6=0;3х +2u-8=0.
9. We see that the coefficient at at is identical on value, but is various according to the sign, therefore, if we put these equations, then at all we will get rid from at: 4th to a +3kh-2 +2u-6-8=0;7kh-14=0; x =2. We substitute value x in any of two equations of a system and we receive at =1.