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Chapter 3

Chapter 3. Section 1 Graphing Systems of Equations. Graph each equation. 1. y = 3 x – 2 2. y = – x 3. y = – x + 4 Graph each equation. Use one coordinate plane for all three graphs. 4. 2 x – y = 1 5. 2 x – y = –1 6. x + 2 y = 2. 1 2. Lesson Preview p. 116.

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Chapter 3

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  1. Chapter 3 Section 1 Graphing Systems of Equations

  2. Graph each equation. 1.y = 3x – 2 2.y = –x3.y = – x + 4 Graph each equation. Use one coordinate plane for all three graphs. 4. 2x – y = 1 5. 2x – y = –1 6.x + 2y = 2 1 2 Lesson Preview p. 116

  3. Lesson Preview Answers 1.y = 3x – 2 2.y = –x slope = 3 slope = –1 y-intercept = –2 y-intercept = 0 3.y = – x + 4 4. 2x – y = 1 slope = – –y = –2x + 1 y-intercept = 4 y = 2x – 1 5. 2x – y = –1 6.x + 2y = 2 –y = –2x – 1 2y = –x + 2 y = 2x + 1 y = – x + 1 1 2 1 2 1 2

  4. Graphing Systems of Equations • Systems of Equations – a set of two or more equations that use the same variable • Linear system – a system where the graph of each equation in a system of two variables is a line • A brace is used to keep the equation system together

  5. Solutions to Systems of Linear Equations • A solution of a system of equations is a set of values for the variables that makes all the equations true. • One way to solve linear systems is by graphing -the solution is the point(s) where the graphs intersect

  6. x + 3y = 2 3x + 3y = –6 Graph the equations and find the intersection. The solution appears to be (–4, 2). x + 3y = 2 3x + 3y = –6 (–4) + 3(2) 2 3(–4) + 3(2) –6 (–4) + 6 2 –12 + 6 –6 2 = 2 –6 = –6 Solve the system by graphing. Here are the equations solved for slope intercept form: Check: Show that (–4, 2) makes both equations true.

  7. Check Understanding p. 117 Step1: Graph the equations (slope-intercept form is nice) Solve by graphing. Check your solution. Step 2: Locate where the two graphs intersect Step 3: Name the coordinate point (1,3) Step 4: Check in both equations for accuracy.

  8. Classifying Systems -by the number of solutions (graphing) • Independent – the system has one solution (only one coordinate pair will work for all equations). These lines intersect in one point.

  9. Dependent – the system has no unique solutions (there is more than one coordinate pair that will work). These are graphed as coinciding lines.

  10. Inconsistent – the system has no solution (no coordinate pair will work). These lines are parallel.

  11. Classify the System Inconsistent No Solution Dependent No Unique Solution (All points of line are solutions) Independent One Solution

  12. Independent – Different slopes m ≠ Dependent – Equal slopes Equal y-intercepts m = b = Inconsistent – Equal slopes Different y-intercepts m = b ≠ Step 1: Solve for slope intercept form Step 2: Write clearly m= and b= for each equation Step 3: Compare slopes and intercepts Classifying Systems without Graphing-comparing slopes and intercepts

  13. y = 3x + 2 –6x + 2y = 4 y = 3x + 2 –6x + 2y = 4 Rewrite in slope-intercept form.y = 3x + 2 m = 3, b = 2 Find the slope and y-intercept. m = 3, b = 2 Classify the system without graphing. Since the slopes are the same, compare the y-intercepts. Since the y-intercepts are the same, the lines are dependent.

  14. Homework

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