Systems of Linear Equations

 

A system of linear equations is a collection of linear equations involving the same set of variables. A system of linear equations means two or more linear equations; two or more lines. If these two linear equations intersect, that point of intersection is called the solution to the system of linear equations. When you are trying to determine if a point is a solution to a set of linear equatios you will run into a few cases; the system has exactly one solution, has no solution, or has infinanate many solutions. When the system has only one solutions means that the two lines have different slopes. When the system has no solutions is when the lines are parallel and have different y- intercepts. And when the system has an infinnte many solutions is when two lines are the same line because of the same slpo, y- intercepts, and are parallel.

A system of equations is a set of two or more equatons that use the same variables. There are three possible solutions to a system of eguations. The first one is the independent syatem which has intercectiong lines and one solution. Then there is the dependent system wich has coinciding (same) lines wich have the same slope and y- intercepts, and has infinitely  many solutions. The last one is inconsistent system wich has parallel lines (same slope, but different y- intercepts) and no solutions. And if you cant graph the equation make sure it is in y=mx+b form.

The process for solving a system of equations using substitution is only if the x or y is by itsself in one of the equations, plug into the other equation and sole. Remember to go back and slove for the other value. And if a varriable is not by itself that move on varriable to the oppisit side of the equation by subtracting.

To solve systems ueing elimination you add two equations with opposite x or y values together in order to eliminate of the variables. There are four steps in solving systems of equations using elimination; multiply each tearm by a number to obtain either opposite x or opposite y values, add the two equations together, solve for the remaining variable, and remember to go back and solve for the other variable.

To solve 3Dimensions using substitution there are six steps:

1.)       Number your equtions

2.)       Solve one equation for one of its variables (try to pick one w/o coefitiant)

3.)       Sub that into the other equations

4.)       Label your new equations with numbers

5.)       Solve using sub/elim

6.)       Solve for other variable

 

 

To solve 3Dimentions using elimination there are also six steps:

1.)       Number equations

2.)       Plain two equations based on easyiest to use elimination with

3.)       Add these two equations

4.)       Relabel new equations

5.)       Solve the two new equations find the other variables