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2 + “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 right into either of the initial equations 9x + 2(-3) = 39 9x - 6 = 39 x = 5 9(5) + 2(-3) = 39 39 = 39 The equipment is the allude (5,-3). Instead of (5,-3) into both equations come check. 6(5) + 13(-3) = -9 -9 = -9

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

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4 Homework Punchline worksheet 8.2DID you HEAR around the antelope who was gaining dressed as soon as he to be trampled by a herd that buffalo? WELL, as much as us know, this was the very first self-dressed, stamped antelope

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5 Homework Punchline worksheet 8.5What go Cate Often call Her twin Sister?? DUPLICATE

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6 Learning Goal finding out TargetStudents will be able to write and graph systems of direct equations. Discovering Target student will have the ability to special varieties systems of direct equations

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7 “How do You fix a linear System???”(1) Solve direct Systems by Graphing (5.1) (2) Solve straight Systems by Substitution (5.2) (3) Solve straight Systems through ELIMINATION!!! (5.3)

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8 Section 5.4 “Solve Special varieties of linear Systems”consists of two or much more linear equations in the same variables. Types of solutions: (1) a single point of intersection – intersecting currently (2) no systems – parallel lines (3) infinitely plenty of solutions – when two equations represent the exact same line

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9 “Solve linear Systems by Elimination” 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 elevation 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 systems is the point (5,3). Instead of (5,3) into both equations come check. -3(5) + 2(3) = -9 -9 = -9

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10 “Solve direct Systems v 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 equipment By looking in ~ the graph, the lines are PARALLEL and therefore will never intersect.

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11 “Solve straight Systems through Infinitely countless Solutions”Equation 1 x – 2y = -4 Equation 2 y = ½x + 2 use ‘Substitution’ because we understand what y is equals. Equation 1 x – 2y = -4 x – 2(½x + 2) = -4 x – x – 4 = -4 This is a true statement, thus the system has infinitely numerous solutions. -4 = -4 “Consistent dependency System” Infinitely countless Solutions by looking at the graph, the lines room the SAME and also therefore crossing at every point, INFINITELY!

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12 + 5x + 3y = 6 -5x - 3y = 3 “Inconsistent System” 0 = 9 No Solution“Tell whether the System has actually No solutions or Infinitely countless Solutions” eliminated Eliminated 5x + 3y = 6 Equation 1 + -5x - 3y = 3 Equation 2 This is a false statement, as such the system has actually no solution. “Inconsistent System” 0 = 9 No equipment

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13 Infinitely numerous Solutions“Tell even if it is the System has No options or Infinitely countless Solutions” Equation 1 -6x + 3y = -12 Equation 2 y = 2x – 4 use ‘Substitution’ since we understand what y is equals. Equation 1 -6x + 3y = -12 -6x + 3(2x – 4) = -12 -6x + 6x – 12 = -12 This is a true statement, because of this the system has actually infinitely countless solutions. -12 = -12 “Consistent dependency System” Infinitely many Solutions

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14 How do You recognize the variety of Solutions of a straight System?First rewrite the equations in slope-intercept form. Then to compare the slope and also y-intercepts.

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Y -intercept slope y = mx + b number of Solutions Slopes and also y-intercepts One solution different slopes No solution exact same slope different y-intercepts Infinitely countless solutions very same y-intercept

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15 “Identify the number of Solutions”Without addressing the straight system, tell whether the system has one solution, no solution, or infinitely plenty of solutions. 5x + y = -2 -10x – 2y = 4 6x + 2y = 3 6x + 2y = -5 3x + y = -9 3x + 6y = -12 Infinitely many solutions No systems One equipment y = -5x – 2 – 2y =10x + 4 y = 3x + 3/2 y = 3x – 5/2 y = -3x – 9 y = -½x – 2

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