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# Module 7 topic 1 notes

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### Module 7 topic 1 notes

1. 1. Systems of Equations<br />
2. 2. Our body systems are interconnected and dependent on <br />each other!<br />It takes all the systems for human <br />growth and development.<br />How is this related to a system of linear equations?<br />The Human Body System<br />
3. 3. In mathematics, a system of linear equations is a collection of 2 or more linear equations involving the same variable.   A SOLUTION to a system is any point (x, y) that makes ALL equations in the system true!<br />Think back to linear equations! <br />Given y = 2x – 3, a "solution" to this equation was any (x, y) point that "worked" in the equation, made the equation TRUE!<br />y = 2x – 3<br />1 = 2(2) – 3<br />1 = 4 – 3 <br />1 = 1<br />(2,1) is a solution since the statement is true!<br />
4. 4. These two linear graphs represent the cost of taking a cab around town based on the number of miles driven.The point of intersection is the solution. The point of intersection on this graph is (3,8). Both companies will charge the same amount, \$8 for 3 miles.<br />
5. 5. Graphing is one of many methods used to solve a linear system. <br />Solving Linear Systems by Graphing<br />Solving Linear Systems using GRAPHING<br />
6. 6. Example 1: Solve the linear system by graphing: <br />Linear Systems<br />Intersect at (3,0)<br />
7. 7. Click the Calculator to Learn how to Graph on the Graphing Calculator!<br />
8. 8. Interpreting Solutions<br />The equations must be in slope-intercept form: (y = mx + b)<br />Graph the system.<br />Find the point(s) of intersection.<br /> <br />If they DO NOT INTERSECT …<br />PARALLEL Lines produce NO SOLUTION b/c there are NO POINTS in common!<br />SAME Lines produce MANY SOLUTIONS b/c they share ALL POINTS!<br />
9. 9. Let’s Practice!<br />After reading the material in this topic, it is time to check your knowledge. <br />You may repeat the practice until you have received a score of 80 or above!<br />Once you have successfully completed this assignment, you can move to the Mastery Assignments.<br />I’m ready to Practice!<br />