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Solving systems of linear equations by graphing lecture

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Solving systems of linear equations by graphing lecture

  1. 1. Solving Systems of Linear Equations by Graphing<br />Prepared by KaiyaDuppins<br />
  2. 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‘₯+𝑦=βˆ’5βˆ’7π‘₯+9𝑦=0Β Β Β Β Β Β Β Β Β Β Β Β Β 5π‘₯βˆ’4𝑦=11<br />4π‘₯βˆ’2𝑦=73𝑦=8𝑦=3π‘₯+1<br />Β <br />
  3. 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. 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. 5. No Solution<br />π‘₯βˆ’2𝑦=6<br />βˆ’2π‘₯+4𝑦=4<br />Β <br />
  6. 6. Infinitely Many Solutions<br />2𝑦+6=βˆ’4π‘₯<br />2π‘₯+𝑦=βˆ’3<br />Β <br />
  7. 7. One Solution<br />3π‘₯βˆ’2𝑦=8<br />𝑦=βˆ’π‘₯+6<br />Β <br />
  8. 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‘₯βˆ’2𝑦=8<br />𝑦=βˆ’π‘₯+6<br />Β <br />
  9. 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. 10. Summary<br />

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