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Do Now 1/15/10

Do Now 1/15/10. Copy HW in your planner. Text p. 462, #1-8 all, #10, #12, #16-30 evens, #36 Be ready to finish quiz sections 7.1 – 7.4. You will have 10 minutes. Objective. SWBAT identify the number of solutions of a linear system. “How Do You Solve a Linear System???”.

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Do Now 1/15/10

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  1. Do Now 1/15/10 • Copy HW in your planner. • Text p. 462, #1-8 all, #10, #12, #16-30 evens, #36 • Be ready to finish quiz sections 7.1 – 7.4. You will have 10 minutes.

  2. Objective • SWBAT identify the number of solutions of a linear system

  3. “How Do You Solve a Linear System???” (1) Solve Linear Systems by Graphing (7.1) (2) Solve Linear Systems by Substitution (7.2) (3) Solve Linear Systems by ELIMINATION!!! (7.3) Adding or Subtracting (4) Solve Linear Systems by Multiplying First (7.4) Then eliminate.

  4. Section 7.5 “Solve Special Types of Linear Systems” LINEAR SYSTEM- consists of two or more linear equations in the same variables. Types of solutions: (1) a single point of intersection – intersecting lines (2) no solution – parallel lines (3) infinitely many solutions– when two equations represent the same line

  5. “Solve Linear Systems by Elimination” Multiplying First!!” Multiply First Eliminated x (2) 4x + 5y = 35 8x + 10y = 70 Equation 1 + x (-5) 15x - 10y = 45 -3x + 2y = -9 Equation 2 23x = 115 “Consistent Independent System” x = 5 4x + 5y = 35 Equation 1 Substitute value for x into either of the original equations 4(5) + 5y = 35 20 + 5y = 35 y = 3 4(5) + 5(3) = 35 35 = 35 -3(5) + 2(3) = -9 -9 = -9 The solution is the point (5,3). Substitute (5,3) into both equations to check.

  6. “Solve Linear Systems with No Solution” Eliminated Eliminated 3x + 2y = 10 Equation 1 _ + -3x + (-2y) = -2 3x + 2y = 2 Equation 2 This is a false statement, therefore the system has no solution. 0 = 8 “Inconsistent System” No Solution By looking at the graph, the lines are PARALLEL and therefore will never intersect.

  7. “Solve Linear Systems with Infinitely Many Solutions” x – 2y = -4 Equation 1 y = ½x + 2 Use ‘Substitution’ because we know what y is equals. Equation 2 Equation 1 x – 2y = -4 x – 2(½x + 2) = -4 x – x – 4 = -4 This is a true statement, therefore the system has infinitely many solutions. -4 = -4 “Consistent Dependent System” Infinitely Many Solutions By looking at the graph, the lines are the SAME and therefore intersect at every point, INFINITELY!

  8. “Tell Whether the System has No Solutions or Infinitely Many Solutions” Eliminated Eliminated 5x + 3y = 6 Equation 1 + -5x - 3y = 3 Equation 2 This is a false statement, therefore the system has no solution. “Inconsistent System” 0 = 9 No Solution

  9. “Tell Whether the System has No Solutions or Infinitely Many Solutions” -6x + 3y = -12 Equation 1 y = 2x – 4 Use ‘Substitution’ because we know what y is equals. Equation 2 Equation 1 -6x + 3y = -12 -6x + 3(2x – 4) = -12 -6x + 6x – 12 = -12 This is a true statement, therefore the system has infinitely many solutions. -12 = -12 “Consistent Dependent System” Infinitely Many Solutions

  10. How Do You Determine the Number of Solutions of a Linear System? • First rewrite the equations in slope-intercept form. • Then compare the slope and y-intercepts. y -intercept slope y = mx + b

  11. “Identify the Number of Solutions” • Without solving the linear system, tell whether the system has one solution, no solution, or infinitely many solutions. 5x + y = -2 -10x – 2y = 4 6x + 2y = 3 6x + 2y = -5 3x + y = -9 3x + 6y = -12 Infinitely many solutions No solution One solution y = -5x – 2 – 2y =10x + 4 y = -5x – 2 y = 3x + 3/2 y = 3x – 5/2 y = -3x – 9 y = -½x – 2

  12. WAR!!“Identify the Number of Solutions” • Without solving the linear system, tell whether the system has one solution, no solution, or infinitely many solutions.

  13. Homework NJASK7 Prep • Text p. 462, #1-8 all, #10, #12, #16-30 evens, #36

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