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- 1. Solving Systems of Linear Equations by Graphing<br />Prepared by KaiyaDuppins<br />
- 2. What is a system of linear equations?<br />Linear equation- an equation that uses only first order variables<br />System of equations- two or more equations, each of which contains at least one variable<br />Examples of System of Linear Equations aka System<br />3π₯+π¦=β5β7π₯+9π¦=0Β Β Β Β Β Β Β Β Β Β Β Β Β 5π₯β4π¦=11<br />4π₯β2π¦=73π¦=8π¦=3π₯+1<br />Β <br />
- 3. How do you solve a system by graphing?<br />Write each equation in slope intercept form y=mx+b<br />Graph each line on the graph<br />Examine the graph to determine the type of solution. <br />Examine the graph to determine the solution and record it. <br />
- 4. Types of Solutions<br />One Solution- if the lines intersect, the point of intersection is the solution (these are not always whole numbers)<br />No Solution-if the lines are parallel and distinct, the linear system does not have a solution<br />Infinitely Many Solutions-if the lines coincide, then every point on the line is a solution<br />Coincide-the graphs of two equations are identical; one line on top of the other<br />
- 5. No Solution<br />π₯β2π¦=6<br />β2π₯+4π¦=4<br />Β <br />
- 6. Infinitely Many Solutions<br />2π¦+6=β4π₯<br />2π₯+π¦=β3<br />Β <br />
- 7. One Solution<br />3π₯β2π¦=8<br />π¦=βπ₯+6<br />Β <br />
- 8. How to check your solution?<br />If there is only one solution to the system then it is said to satisfythe system.<br />Check to see if the solution you derived satisfies the system.<br />Evaluate the system using the solution. (plug in the numbers)<br />3π₯β2π¦=8<br />π¦=βπ₯+6<br />Β <br />
- 9. Interpreting the Graph<br />Dependent- the graphs of two equations are identical ; the equations can be derived from one another<br />Independent-the graphs of two equations are distinct<br />Consistent- a system that has at least one solution<br />Inconsistent- a system that has no solutions<br />
- 10. Summary<br />

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