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# Linear Systems

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### Linear Systems

1. 1. System’s of Linear Equations Donald Saunders
2. 2. What is it and how do we solve it? <ul><li>Two or more linear equations that are grouped together </li></ul><ul><li>A solution is an ordered pair that is a solution of ALL equations in a system </li></ul><ul><li>There are three methods commonly used to solve a system of linear equations </li></ul>
3. 3. Three methods used to solve <ul><li>Substitution </li></ul><ul><li>Graphing </li></ul><ul><li>Elimination </li></ul>
4. 4. Substitution Method We will be substituting part of one equation into the other equation <ul><li>y = x and x + y = 2 </li></ul><ul><li>x + x = 2 remove the y in the second equation and replace it with x from the first equation </li></ul><ul><li>2x = 2 combine like terms </li></ul><ul><li>x = 1 solve for x </li></ul><ul><li>y = x = 1 plug in what x equals and solve for y in either equation </li></ul><ul><li>(1, 1) identify the solution to our system of equations </li></ul>
5. 5. Graphing Method A linear system of equations are two lines. Let’s graph our lines to see what happens. y = x and x + y = 2
6. 6. Graphing Method Remember our solution was (1,1), so let’s identify this on our graph and deduce how we can identify our solution using the graphing method
7. 7. How can we identify the solution to a system of linear equations if we graph them? <ul><li>The point where the line crosses the x-axis </li></ul><ul><li>The point where the line crosses the y-axis </li></ul><ul><li>The point where the two lines cross each other </li></ul>
8. 8. Elimination method <ul><li>Eliminates one variable from the equations </li></ul><ul><li>Can be either variable </li></ul><ul><li>Key is to get the same number with opposite signs for either variable </li></ul><ul><li>Once you have solved for one variable, you can plug that value in and solve for the second variable </li></ul>
9. 9. Elimination Method <ul><li>y = x and x + y = 2 </li></ul><ul><li>x + y = 0 </li></ul><ul><li>x + y = 2 </li></ul><ul><li>2y = 2 </li></ul><ul><li>y = 1 </li></ul><ul><li>x + (1) = 2 </li></ul><ul><li>x = 1 </li></ul><ul><li>(1, 1) </li></ul>
10. 10. Who prefers which method?
11. 11. More Practice If you need more practice you can go to the J lab website
12. 12. References <ul><li>http://education.jlab.org/solquiz/index.html </li></ul><ul><li>http://player.discoveryeducation.com/index.cfm?guidAssetId=BF5C2DD4-437B-4F0D-B5C6-B90AF853C30E </li></ul>
13. 13. Correct <ul><li>The solution to a system of equations that has been graphed is the point at which they intersect. If they do not intersect there is No Solution, and if the two lines lie on top of each other there are Infinite Solutions. </li></ul><ul><li>Back to presentation </li></ul>
14. 14. Incorrect The y-axis and x-axis have nothing to do with the solution. These are only points used to graph our two lines Back to Quiz