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## Solving Systems of Equations 3 Approaches

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**Solving Systems of Equations**3 Approaches Click here to begin Mrs. N. Newman**Method #1**Graphically Door #1 Method #2 Algebraically Using Addition and/or Subtraction Door #2 Method #3 Algebraically Using Substitution Door #3**In order to solve a system of equations graphically you**typically begin by making sure both equations are in standard form. Where m is the slope and b is the y-intercept. Examples: y = 3x- 4 y = -2x +6 Slope is 3 and y-intercept is - 4. Slope is -2 and y-intercept is 6.**Graph the line by locating the appropriate**intercept, this your first coordinate. Then move to your next coordinate using your slope.**Once both lines have been graphed locate the point of**intersection for the lines. This point is your solution set. In this example the solution set is[2,2].**In order to solve a system of equations algebraically using**addition first you must be sure that both equation are in the same chronological order. Example: Could be**Now select which of the two variables you want to eliminate.**For the example below I decided to remove x. The reason I chose to eliminate x is because they are the additive inverse of each other. That means they will cancel when added together.**Now add the two equations together.**Your total is: therefore**Now substitute the known value into either one of the**original equations. I decided to substitute 3 in for y in the second equation. Now state your solution set always remembering to do so in alphabetical order. [-1,3]**Lets suppose for a moment that the equations are in the same**sequential order. However, you notice that neither coefficients are additive inverses of the other. Identify the least common multiple of the coefficient you chose to eliminate. So, the LCM of 2 and 3 in this example would be 6.**Multiply one or both equations by their respective**multiples. Be sure to choose numbers that will result in additive inverses. becomes**Now add the two equations together.**becomes Therefore**Now substitute the known value into either one of the**original equations.**Now state your solution set always remembering to do so in**alphabetical order. [-3,3]**In order to solve a system equations algebraically using**substitution you must have on variable isolated in one of the equations. In other words you will need to solve for y in terms of x or solve for x in terms of y. In this example it has been done for you in the first equation.**Now lets suppose for a moment that you are given a set of**equations like this.. Choosing to isolate yin the first equation the result is :**Now substitute what yequals into the second equation.**becomes Better know as Therefore**This concludes my presentation on simultaneous equations.**Please feel free to view it again at your leisure.