Systems

Systems of equations is a set or collection of equations that you deal with all together at once. There are three ways to solve linear equations, there is Graphing, Subsituting and Elminating. If you want to graph a linear equation, you have two equations with the basic formula y=mx+b M=Slope and B=y-intercept, that represent what you are graphing. If the lines interesect once there is only one solution, if there dont interesect there is no solution, and if there are on top of eachother there is infinite solutions. As shown below.

You can also find inequalities by finding there shaded region and where they over lap. For Example:

The Subsitution Method, still uses the y=mx+b formula with two equations, but instead of the graphing you try to get __Y__ by itself. While getting y alone on one side of the equation you subsitute that y for the y in the other equation, as shown below.

Solving Sytems by Elimination is one of the most common to use. Variables must be lined up and one must be able to cancel out. When cancelinghi h

__Systems:__ Systems are a group of equations __Intersecting Lines:__ Intersecting Lines are lines that meet eachother at the same point __Elimination:__ Elimination gets X, or Y to be opposite of eachother to cancel eachother out to find the X, or Y. __Subsitution__: Get X or Y by itself to subsitution it equation inside the other to distribute the X, or Y to find X, or Y. __Graphing__: Finds where graphs of lines intercepts
 * 5 Key Terms:**

Another example for Solving Systems by graphing can be shown below:

There are 30 students in Mrs.Jones class. If the number of girls is 3 less than twice the number of boys, how many boys are in Mrs. Jones class.
 * Word Problem:**

x = boys y = girls

a. x + y = 30 b. y = 2x - 3

Substitutue b. into a. x + 2x - 3 = 30 3x = 33 x = 11

use that in either equation y = 2*11 - 3 = 19

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