Presentation on theme: "Solving Systems of Equations"— Presentation transcript:
1Solving Systems of Equations 3 ApproachesClick here to beginMrs. N. Newman
2Method #1GraphicallyDoor #1Method #2Algebraically Using Addition and/or SubtractionDoor #2Method #3Algebraically Using SubstitutionDoor #3
3In 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- 4y = -2x +6Slope is 3 and y-intercept is - 4.Slope is -2 and y-intercept is 6.
4Graph the line by locating the appropriate intercept, this your first coordinate. Then move to your nextcoordinate using your slope.
6Once 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].
7In 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
8Now 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.
9Now add the two equations together. Your total is:therefore
10I decided to substitute 3 in for y in the second equation. 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]
11Lets 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.
12Multiply one or both equations by their respective multiples Multiply one or both equations by their respective multiples. Be sure to choose numbers that will result in additive inverses.becomes
13Now add the two equations together. becomesTherefore
14Now substitute the known value into either one of the original equations.
15Now state your solution set always remembering to do so in alphabetical order. [-3,3]
16In this example it has been done for you in the first equation. 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.
17Choosing to isolate y in the first equation the result is : Now lets suppose for a moment that you are given a set of equations like this..Choosing to isolate y in the first equation the result is :
18Now substitute what y equals into the second equation. becomesBetter know asTherefore
19This concludes my presentation on simultaneous equations. Please feel free to view it again at your leisure.