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We will primarly dealing with systems of equations in two variable (i.e. equations with an x and y). We will work only with 2 equation systems.
Solving systems of linear equations by graphing lecture
Solving Systems of Linear Equations by Graphing<br />Prepared by KaiyaDuppins<br />
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 />3𝑥+𝑦=−5−7𝑥+9𝑦=0 5𝑥−4𝑦=11<br />4𝑥−2𝑦=73𝑦=8𝑦=3𝑥+1<br /> <br />
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 />
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 />
No Solution<br />𝑥−2𝑦=6<br />−2𝑥+4𝑦=4<br /> <br />
Infinitely Many Solutions<br />2𝑦+6=−4𝑥<br />2𝑥+𝑦=−3<br /> <br />
One Solution<br />3𝑥−2𝑦=8<br />𝑦=−𝑥+6<br /> <br />
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 />3𝑥−2𝑦=8<br />𝑦=−𝑥+6<br /> <br />
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 />