Presentation on theme: "Solving Systems of Equations"— Presentation transcript:
1Solving Systems of Equations 3 ApproachesClick here to beginMs. NongAdapted from Mrs. N. Newman’s PPT
2Method #1GraphicallyPOSSIBLE ANSWER:Answer: (x, y)or (x, y, z)Method #2Algebraically Using Addition and/or SubtractionAnswer: No SolutionAnswer: IdentityMethod #3Algebraically Using Substitution
3In order to solve a system of equations graphically you typically begin by making sure both equations are in Slope-Intercept 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.
5Looking at the System Graphs: If the lines cross once, therewill be one solution.If the lines are parallel, therewill be no solutions.If the lines are the same, therewill be an infinite number of solutions.
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 one 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
19Lets look at another Systems solve by Substitution
20Step 5: Check the solution in both equations. y = 4x3x + y = -21Step 5: Check the solution in both equations.3x + y = -213(-3) + (-12) = -21-9 + (-12) = -21-21= -21y = 4x-12 = 4(-3)-12 = -12
21This concludes my presentation on simultaneous equations. Please feel free to view it again at your leisure.