Do Now 12/14/18 y = 2x + 5 3x + y = 10 9x + 2y = 39 6x + 13y = -9 Take out HW from last night. Punchline worksheets 8.2 & 8.5 Copy HW in your planner. Text p. 257, #4-24 evens, 25 Quiz sections 5.1-5.4 Tuesday In your notebook, explain the 3 different methods there are for solving a system. Then identify which method you use to solve the systems below. Solve each system. y = 2x + 5 3x + y = 10 9x + 2y = 39 6x + 13y = -9

+ “Solve Linear Systems by Elimination Multiplying First!!” Eliminated x (2) 9x + 2y = 39 18x + 4y = 78 Equation 1 + x (-3) -18x - 39y = 27 6x + 13y = -9 Equation 2 -35y = 105 y = -3 9x + 2y = 39 Equation 1 Substitute value for y into either of the original equations 9x + 2(-3) = 39 9x - 6 = 39 x = 5 9(5) + 2(-3) = 39 39 = 39 The solution is the point (5,-3). Substitute (5,-3) into both equations to check. 6(5) + 13(-3) = -9 -9 = -9

“Solve Linear Systems by Substituting” y = 2x + 5 Equation 1 3x + y = 10 Equation 2 3x + y = 10 3x + (2x + 5) = 10 Substitute 3x + 2x + 5 = 10 5x + 5 = 10 x = 1 y = 2x + 5 Equation 1 Substitute value for x into the original equation y = 2(1) + 5 y = 7 (7) = 2(1) + 5 7 = 7 The solution is the point (1,7). Substitute (1,7) into both equations to check. 3(1) + (7) = 10 10 = 10

Homework Punchline worksheet 8.2 DID YOU HEAR ABOUT the antelope who was getting dressed when he was trampled by a herd of buffalo? WELL, as far as we know, this was the first self-dressed, stamped antelope

Homework Punchline worksheet 8.5 What Does Cate Often Call Her Twin Sister?? DUPLICATE

Learning Goal Learning Target Students will be able to write and graph systems of linear equations. Learning Target Students will be able to special types systems of linear equations

“How Do You Solve a Linear System???” (1) Solve Linear Systems by Graphing (5.1) (2) Solve Linear Systems by Substitution (5.2) (3) Solve Linear Systems by ELIMINATION!!! (5.3)

Section 5.4 “Solve Special Types of Linear Systems” 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

“Solve Linear Systems by Elimination” Multiplying 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 The solution is the point (5,3). Substitute (5,3) into both equations to check. -3(5) + 2(3) = -9 -9 = -9

“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.

“Solve Linear Systems with Infinitely Many Solutions” Equation 1 x – 2y = -4 Equation 2 y = ½x + 2 Use ‘Substitution’ because we know what y is equals. 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!

+ 5x + 3y = 6 -5x - 3y = 3 “Inconsistent System” 0 = 9 No Solution “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

Infinitely Many Solutions “Tell Whether the System has No Solutions or Infinitely Many Solutions” Equation 1 -6x + 3y = -12 Equation 2 y = 2x – 4 Use ‘Substitution’ because we know what y is equals. 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

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 Number of Solutions Slopes and y-intercepts One solution Different slopes No solution Same slope Different y-intercepts Infinitely many solutions Same 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. 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 = 3x + 3/2 y = 3x – 5/2 y = -3x – 9 y = -½x – 2

What Did You Learn?

PARCC Prep Homework Text p. 257, #4-24 evens, 25