The linear system with three unknown has several ways of the decision. It is possible to find a solution of a system by means of Kremer's rule through determinants, by Gauss's method or using an easy way of substitution. The method of substitution is the basic for the solution of systems of the linear equations of a small order. It consists in serial expression from each equation of a system of one unknown variable, its substitution in the following equation and simplification of the received expressions.
Instruction
1. Write down the initial system of the equations the third about. From the first equation of a system express the first unknown variable x. For this purpose transfer the members containing other variables for an equal-sign. To the postponed members change the sign for opposite.
2. If at a multiplier from the expressed variable there is a coefficient other than unit, divide all equation into its value. Thus, you receive a variable x, expressed through other members of the equation.
3. Substitute in the second equation instead of x that expression which you received from the first equation. Simplify the received record, having made addition or subtraction of similar members. Express to similarly previous step from the second equation the following unknown variable at. Also transfer everything other members for an equal-sign and divide all equation into coefficient at at.
4. In the last third equation substitute instead of two unknown variables x and at the expressed values from the first and second equations of a system. And in expression x also replace a variable at. Simplify the received equation. In it as unknown size there will be third variable z. Express it from the equation as it is described above, and calculate its value.
5. In expression at from the second equation substitute the known value of variable z. Count value of a variable at. Further in expression of a variable x substitute values of variables at and z. Calculate x. Write down the received values x, at and z is and there is a solution of a system with three unknown.