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WARM-UP

3.1. 1. 2. 3. 4. 5. 6. WARM-UP. Graph each of the following problems. 3.1. Solve Linear Systems by Graphing. A system of linear equations is 2 or more equations that intersect at the same point or have the same solution.

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WARM-UP

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  1. 3.1 1. 2. 3. 4. 5. 6. WARM-UP Graph each of the following problems

  2. 3.1 Solve Linear Systems by Graphing A system of linear equations is 2 or more equations that intersect at the same point or have the same solution. You can find the solution to a system of equations in several ways. The one you are going to learn today is to find a solution by graphing. The solution is the ordered pair where the 2 lines intersect. In order to solve a system, you need to graph both equations on the same coordinate plane and then state the ordered pair where the lines intersect.

  3. Classifying Systems • Consistent – a system that has at least one solution • Inconsistent – a system that has no solutions • Independent – a system that has exactly one solution • Dependent – a system that has infinitely many solutions Lines intersect at one point: consistent and independent Lines coincide; consistent and dependent Lines are parallel; inconsistent

  4. Graph each system and then estimate the solution. GUIDED PRACTICE • 4x – 5y = -10 • 2x – 7y = 4 • 3x + 2y = -4 • x + 3y = 1 4x – 5y = -10 2x – 7y = 4 3x + 2y = -4 x + 3y = 1 -7y = -2x + 4 -5y = -4x -10 3y = -x + 1 2y = -3x - 4 From the graph, the lines appear to intersect at (–2, 1). From the graph, the lines appear to intersect at (–5, –2). Consistent & Independent Consistent & Independent

  5. GUIDED PRACTICE • 8x – y = 8 • 3x + 2y = -16 8x – y = 8 3x + 2y = -16 -y = -8x + 8 2y = -3x - 16 y = 8x - 8 From the graph, the lines appear to intersect at (0, –8). Consistent & Independent

  6. 4x – 3y = 8 8x – 6y = 16 y = -2x + 1 y = -2x + 4 The system has infinite solutions consistent and dependent. Solve the system. Then classify the system as consistent and independent,consistent and dependent, or inconsistent. 2x + y = 4 2x + y = 1 2x + y = 4 2x + y = 1 4x – 3y = 8 8x – 6y = 16 – 3y = -4x + 8 – 6y = -8x + 16 (the lines have the same slope) (the equations are exactly the same) the system has no solution inconsistent.

  7. 2x + 5y = 6 A. 4x + 10y = 12 3x – 2y = 10 B. 3x – 2y = 2 – 2x + y = 5 C. y = – x + 2 y = – x + 2 y = 2x + 5 Solve the system. Then classify the system as consistent and independent, consistent and dependent, or inconsistent. 2x + 5y = 6 4x + 10y = 12 Same equation Infinite solutions Consistent and independent 10y = -4x + 12 5y = -2x + 6 3x – 2y = 10 3x – 2y = 2 Same slope // lines no solution inconsistent 2y = – 3x + 10 2y = – 3x + 2 (–1, 3) consistent independent – 2x + y = 5

  8. – 2x + y = 5 C. y = – x + 2 y = – x + 2 y = 2x + 5 (–1, 3) consistent independent – 2x + y = 5 Is (-1,3) the correct solution? – 2x + y = 5 y = – x + 2 3 = – (-1)+ 2 – 2(-1)+ (3)= 5 3 = 1+ 2 ☺ 2+ 3 = 5 ☺ HOMEWORK 3.1 P.156 #3-10 and board work

  9. (3, 3) No solution (-1, 1) Infinite solutions

  10. no solution 5. 6. inconsistent, 8. (-1, 3) 7. Infinite solutions Consistent, independent (1, 2) y = 3x - 2 Consistent, dependent No solutions Consistent, independent 11. Infinite solutions y = x + 6 y = x + 5 y= -x + 6 y = -x + 6 12. Inconsistent (2, 1) Consistent, dependent 9. Infinite solutions 13. 14. y = 1/2x + 4 y = ½ x Consistent, dependent 10. Consistent, independent (2, 0) y = -x + 2 y = -x + 6 No solutions y = -2x + 4 y = x - 2 Infinite solutions 15. 16. Consistent, independent inconsistent (1, 1) y = -2x + 4 y = 6x - 4 y = -3x + 2 Consistent, dependent Consistent, independent Solve each system of equations by graphing. Indicate whether the system is Consistent- Independent, Consistent-Dependent, or Inconsistent 5. 6. 8. 7. 10. 9. 12. 11. 14. 13. 16. 15.

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