Math equation

In real life we sometimes face such times of tasks solution of which need the knowledge of solving systems of linear equations in three variables . First of all you should understand what is an equation in three variables . For example , you may have such an object : x 3y 6 This object we call linear equation in two variables . Here x , y are two variables . The word equation ' in this name means that we have equality between x 3y (left side ) and 6 (right side . The word linear ' means that the object defines a

particular straight line on plane xy . The equation x 3y z 6 is similar in form , and so it is a linear equation in three variables . An equation in three variables is graphed in three-dimensional coordinate system . The graph of a linear equation in three variables is a plane , not a line

Generally , if A , B , C , and D are real numbers , with A , B , and C not all zero , then

Ax By Cz D (1

is called a linear equation in three variables

You may notice , that there are many (telling the truth , infinitely many set of numbers x , y , z that satisfy linear equation in three variables For example we can easily check that sets

x 0 , y 1 , z 3

x 3 , y 0 , z 3

x 3 , y 1 , z 0

are solutions to the equation x 3y z 6

Hence , a solution to an equation in three variables is an ed triple such as (0 , 1 , 3 , where the first coordinate is the value of x , the second coordinate is the value of y , and the third coordinate is the value of z . The other two solutions we shall present in form (3 , 0 , 3 and (3 , 1 , 0

When you have to solve a system of three linear independent equations (system of three linear independent equations consists of three equations of type (1 , you need to find such triples that satisfy all three equations simultaneously . In overall there are three possible cases

The system may have a single solution (we call it ed triple

The system may have infinitely many solutions

The system may have no solutions

Now I will teach you haw to solve the system with a single solution and I will show you by examples how we can find the solution for such system of equations . I want you to solve the equation using the addition method . I have three sets of equations that I want you to use

In the addition method we eliminate a variable by adding the equations So how it works ? Let us take the first set of equations that is Example 1

x 3y z 6 (1

3x y - z -2 (2

2x 2y - z 1 (3

The addition property of equality allows you to add the same number to each side of an equation . You can also use the addition property of equality to add the two left sides and the two...