By: Drew Valentine &Tony Williams System Of Equations Elimination Method Objectives Graphing Method Substitution Method Substitution method is the method where you solve for one of the variables and then substitute that variable back in the other equation and solve for the other equation. What are systems of equations? System of equations are a set or collection of equations that you deal with all together at once. To learn how to solve system of equations To learn about system of equations. There are three methods used to solve systems of equations. These methods are: Substitution

Elimination

Graphing Example:

x=2y-10

5=y+x 5=2y+(y-10) 5=3y-10 15=3y __ __ 5=y 5=5+x x=0 3 3 Step 1: Substitute the variable that you know into the other equation. Step 2: Solve for the unknown

variable Step 3: Plug the answer you just found back into one of the equations and solve for the other variable Step 4: Put your answer in (x,y) format. (0,5) In this way of solving systems of equations, one variable is eliminated by adding or subtracting the equations. 2x+y=10

-2x+2y=5

3y=15 __ __ 3 3 y=5 2x+5=10 -5 -5 2x=5 __ _ 2 2 x=2.5 Example: 2x+y=10

-2x+2y=5 3y=15 __ __ 3 3 y=5 2x+5=10 -5 -5 2x=5 __ _ 2 2 x=2.5 (2.5,5) Step 1: Cancel out the two variables that have the opposite coefficient.

Step 2: Solve for the remaining variable

Step 3: Plug the known variable back into either equation and solve

Step 4: Put answer in (x,y) format. To solve a system of equations graphically, graph both equations and see where they intersect. The intersection point is the solution. Example: 4x - 6y = 12

2x + 2y = 6 First Step: Get the equation into y=mx+b form Second Step: Graph the two lines and find out the point of intersection

Third Step: The point of intersection is your final answer. y=2/3x-2

y=-x+3 (3,0) Any Questions?

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# System of Equations

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