ALGEBRA+l

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[|Algebra help]

I. Solving Systems by Graphing.
a. Definition: A //**system of linear equations**// is formed by grouping together two or more linear equations that contain two or more of the same variables: //y// = 3//x// – 2 //y// = –//x// – 6 b. Definition: A **//solution of a system of equations//** is any point that lies on each line in the system. c. [|Graphing Technique]: 1) First, [|graph each line] on the same coordinate plane. Some students find the easiest way to do this is to convert all equations into slope-intercept form if they aren't given to you that way. 2) Second, find the point of intersection of the lines that were graphed in step 1. This point of intersection lies on both of the lines, and fits our definition of a solution of a system of equations. 3) Check your solution by substituting the //x// and //y// coordinates into both of the original equations and simplifying. d. Analyze special cases. e. Apply real world situation.

V. Systems of Linear Inequalities.
Graphing Systems of Linear Inequalities Definition: A **//system of linear inequalities//** is two or more inequalities using the same variables. a) When dividing by a negative, flip the direction of the inequality. b)<,>graph using dashed lines c) ≤,≥graph using solid lines
 * *Remember* **

1. If both inequalities are not already in slope-intercept form, transform the inequalities to slope-intercept form. Ex.)  y≤x+2 ←already in slope-intercept form 2x+3y>-6 ←needs to be transformed __-2x -2x __ subtract 2x from both sides 3y>-2x-6 divide each term by 3 y>-2/3 x-2 2.) Graph the first inequality and shade in the appropriate region: >,≥ shade above the line <span style="font-family: Arial,sans-serif; font-size: 12pt;"><,≤ shade below the line <span style="font-family: Arial,sans-serif; font-size: 12pt;">3.) Graph the second inequality and shade in the appropriate region. <span style="font-family: Arial,sans-serif; font-size: 12pt;">*Check your work by substituting an ordered pair into both inequalities.
 * <span style="font-family: Arial,sans-serif; font-size: 12pt;">Solving Method: **
 * <span style="font-family: Arial,sans-serif; font-size: 12pt;">Solutions: **<span style="font-family: Arial,sans-serif; font-size: 12pt;"> The area where the two shaded regions intersect.
 * <span style="font-family: Arial,sans-serif; font-size: 12pt;">See it in action: **
 * Video **


 * You try!**

VI. Solving Proportions.
Definition: A proportion is a comparison between two ratios. To solve you will cross multiply. Example: 5/4 = x/12 5*12 = 4*x 60 = 4x 60/4 = 4x/4 x = 15 Video [|Solving Proportions]