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2 + “Solve Liclose to Equipment 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 worth for y right 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) right into both equations to examine. 6(5) + 13(-3) = -9 -9 = -9

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3 “Solve Linear Solution 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 allude (1,7). Substitute (1,7) right into both equations to examine. 3(1) + (7) = 10 10 = 10

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4 Homework-related Punchline worksheet 8.2DID YOU HEAR ABOUT the antelope who was obtaining dressed once he was trampled by a herd of buffalo? WELL, as far as we recognize, this was the first self-dressed, stamped antelope

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

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6 Learning Goal Learning TargetStudents will certainly be able to create and also graph systems of straight equations. Learning Target Students will certainly be able to one-of-a-kind kinds systems of direct equations

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

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8 Section 5.4 “Solve Special Types of Linear Systems”consists of 2 or even more straight equations in the very same variables. Types of solutions: (1) a single point of interarea – intersecting lines (2) no solution – parallel lines (3) infinitely many options – when 2 equations reexisting the very same line

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9 “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 worth 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 suggest (5,3). Substitute (5,3) into both equations to check. -3(5) + 2(3) = -9 -9 = -9

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10 “Solve Liclose to Solution 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 device has no solution. 0 = 8 “Inconstant System” No Equipment By looking at the graph, the lines are PARALLEL and therefore will certainly never intersect.

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11 “Solve Liclose to Equipment via Infinitely Many Solutions”Equation 1 x – 2y = -4 Equation 2 y = ½x + 2 Use ‘Substitution’ bereason we recognize what y is amounts to. Equation 1 x – 2y = -4 x – 2(½x + 2) = -4 x – x – 4 = -4 This is a true statement, therefore the device has actually infinitely many type of options. -4 = -4 “Consistent Dependent System” Infinitely Many type of Solutions By looking at the graph, the lines are the SAME and therefore intersect at eexceptionally allude, INFINITELY!

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12 + 5x + 3y = 6 -5x - 3y = 3 “Inconstant System” 0 = 9 No Solution“Tell Whether the System has No Solutions or Infinitely Many type of Solutions” Eliminated Eliminated 5x + 3y = 6 Equation 1 + -5x - 3y = 3 Equation 2 This is a false statement, therefore the device has actually no solution. “Incontinual System” 0 = 9 No Solution

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13 Infinitely Many type of Solutions“Tell Whether the System has No Solutions or Infinitely Many type of Solutions” Equation 1 -6x + 3y = -12 Equation 2 y = 2x – 4 Use ‘Substitution’ because we understand what y is amounts to. Equation 1 -6x + 3y = -12 -6x + 3(2x – 4) = -12 -6x + 6x – 12 = -12 This is a true statement, therefore the mechanism has actually infinitely many type of options. -12 = -12 “Consistent Dependent System” Infinitely Many Solutions

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14 How Do You Determine the Number of Solutions of a Linear System?First recreate the equations in slope-intercept form. Then compare the slope and 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 Same slope Different y-intercepts Infinitely many kind of services Same y-intercept

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

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