Do Now 1/15/10 Copy HW in your planner. Copy HW in your planner. Text p. 462, #1-8 all, #10, #12, #16-30 evens, #36 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. 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 SWBAT identify the number of solutions of a linear system

“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.

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

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

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

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

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

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

How Do You Determine the Number of Solutions of a Linear System? Number of Solutions Slopes and y-intercepts One solution Different slopes No solution Same slope Different y-intercepts Infinitely many solutions Same slope Same y-intercept (1)First rewrite the equations in slope-intercept form. (2)Then compare the slope and y-intercepts. y = mx + b slope y -intercept

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

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

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