## The method of substitution

To understand the essence of this method is easiest on the example of solving a typical system includes two equations and requires finding the values of the two unknowns. So, this may be the following system consisting of the equations x + 2y = 6 and x - 3y = -18. In order to solve it by the method of substitution is required in any of the equations to Express one member through another. For example, this can be done using the first equation: x = 6 - 2y.

You must then substitute the resulting expression into the second equation instead of x. The result of this lookup will be the equality of 6 - 2y - 3y = -18. By performing simple arithmetic calculations, this equation is easy to lead to standard view 5y = 24 where y = 4,8. Then the value obtained should be substituted in the expression used for the lookup. Hence x = 6 - 2*4,8 = -3,6.

Then it is advisable to verify the obtained results, substituting them in both equations of the original system. This will give the following equations: -3,6 + 2*4,8 = 6 and -3,6 - 3*4,8 = -18. Both of these equality are true, so you can conclude that the system is solved correctly.