Lesson 15 Linear Equations

GOLD 1Gold VocabularyDefinition Example All RealsConsistentDependentDifferenceElimination methodInconsistentNo Solution ProductQuotientSubstitution Method SumSystem of EquationsAlgebra One: Unit Five ~ System of Equations desotocountyschools.org/shs Maggie Dennis & Karen Hatch GOLD 2Lesson 17 Solving Systems of Equations Graphing NotesSolution Possibilities 1. (2,1)2.3.Algebra One: Unit Five ~ System of Equations desotocountyschools.org/shs Maggie Dennis & Karen Hatch GOLD 3Lesson 17 Solving Systems of Equations Graphing Notes y 10 Example One Draw a line with a slope of -3. Draw the graph of a line that is perpendicular to your first line. Write the equation of the perpendicular line.-10 10 x-10 y 10 Example Two Graph two lines that intersect at the point (1,4). Write the equations of your lines.-10 10 x-10 y 10 Example Three x - 3y = -3 y = 2x - 4-10 10 x-10Algebra One: Unit Five ~ System of Equations desotocountyschools.org/shs Maggie Dennis & Karen Hatch GOLD 4Lesson 17 Solving Systems of Equations Graphing Notes y 10 Example Four x + y = 0 x + y = 5-10 10 x-10 y 10 Example Five y = 4x + 1 12x - 3y = -3-10 10 x-10 y 10 Example Six y = -2 2x + y = 8-10 10 x-10Algebra One: Unit Five ~ System of Equations desotocountyschools.org/shs Maggie Dennis & Karen Hatch GOLD 5Lesson 17 Solving Systems of Equations GraphingDOK 11. How many solutions? 2. How many solutions? Point of Intersection? Point of Intersection? Write the equation for Write the equation for each line. y each line. y 10 10 x x -10 10 -10 10-10 -10 Change to slope-intercept, graph each equation, and identify the point of intersection by writing it as an ordered pair: 3. y = x + 3 4. 3x – y = 8 -6x + 2y = y-18 y = -x y 10 10-10 10 x -10 10 x-10 -10Algebra One: Unit Five ~ System of Equations desotocountyschools.org/shs Maggie Dennis & Karen Hatch GOLD 6Lesson 17 Solving Systems of Equations Graphing5. Jessica graphed the following two linear equations on a coordinate grid: 5x + 2y = 4 Hint: Graph both lines. 2x + 5y = 4 Which of the following BEST describes the graph of ythe two linear equations? 10A) The two lines are parallel B) The two lines are perpendicular C) The two lines are the sameD) The two lines intersect at one point -10 10 x-106. Two lines on a coordinate plane have no points of intersection. Which of the following sets of equations could represent the lines? Hint: Graph all lines. A) 3x + 5y = 5 B) 3x + 5y = 5 6x + 10y = 10 6x + 10y = 5C) 3x + 5y = 5 D) 3x + 5y = 5 6x – 10y = 10 y 6x – 10y = 5 10-10 10 x-10 Algebra One: Unit Five ~ System of Equations desotocountyschools.org/shs Maggie Dennis & Karen Hatch GOLD 7Lesson 17 Solving Systems of Equations Graphing7. Which point is a solution for BOTH of the following equations? y = 3x – 2 Hint: Graph both lines. 2y = x + 1 A) (1, 1) B) (2, 4) C) (1, 2) D) (0, -2) y 10-10 10 x-10DOK 2 8. Draw a line with a slope of 2. Write the equation of your line. Draw a line that is perpendicular to your first line on the same coordinate plane. Write the equationy of the perpendicular line. 10-10 10 xAlgebra One: Unit Five ~ System of Equations desotocountyschools.org/shs Maggie Dennis & Karen Hatch -10 GOLD 8Lesson 17 Solving Systems of Equations Graphing y 10 9. Draw the graph of a line whose equation 3 is y = x – 1. Draw the graph of a line 2 parallel to this line and write the equation of this line. -10 10 x y -10 10 10. Draw the graph of a line whose equation 5 is y =  x. Draw the graph of a line 2 perpendicular to this line and write the -10 10 x equation of this line. y 10 -10 11. Graph two lines that intersect at the point (-2, 3). Write the equations of your lines.-10 10 x y 10 -1012. Graph two lines that are perpendicular to one another and intersect at the origin.-10 10 xAlgebra One: Unit Five ~ System of Equations desotocountyschools.org/shs Maggie Dennis & Karen Hatch -10 GOLD 9Lesson 23 Solving Systems of Inequalities Notes The solution to a system of inequalities is not a single ordered pair, but a region of the coordinate plane.Recall when graphing inequalities we must shade. Example One The solution will be the intersection of the two shaded y > -x + 3 y < (1/4)x - 2 regions. y 10Example Two 2y + 2x < 6 y > 2x + 2 -10 10 x-10 y 10Example Three-10 10 x 3x + 8y > 40 4x - 3y > 6-10 y 10-10 10 xAlgebra One: Unit Five ~ System of Equations desotocountyschools.org/shs Maggie Dennis & Karen Hatch -10 GOLD 10Lesson 23 Solving Systems of InequalitiesDOK 1 1. The system of equations 2y = x + 6 and x = -1 is shown on the graph below. Which point satisfies both of the following inequalities, 2y ≤ x + 6 and x ≥ -1? (Hint: add the shading) y 5 a) (-2, 5) b) (-2, 1) x c) (0, 5) -5 5 d) (1, -1)-5Match each system of inequalities toy the correct graph: y 5 5 ____ 2. y < ½ x – 1 y ≤ -2x + 2 A ____ 3. y ≤ ½ x + 1 x B x y > -½ x – 2 -5 5 -5 5____ 4. y ≤ 2x + 2 y > -x – 1 -5 -5 ____ 5. y > x – 2 y y y ≥ -x + 1 5 5 C x x -5 5 -5 5 D Algebra One: Unit Five ~ System of Equations desotocountyschools.org/shs Maggie Dennis & Karen Hatch -5 -5 GOLD 11Lesson 23 Solving Systems of InequalitiesDOK 2 y Graph each system of linear inequalities. 106. y  -2 y < 2x + 1-10 10 x-10y 10 7. y  3x – 2 x  -3-10 10 x-10y 10 8. y – 2x < -3 2x + 3y > 3-10 10 x-10y 9. 4y – x > 8 5x – 2y > 2 10-10 10 x-10 Algebra One: Unit Five ~ System of Equations desotocountyschools.org/shs Maggie Dennis & Karen Hatch GOLD 12Lesson 19 Solving Systems by Substitution NotesUse this method when one of your lines is vertical (y= ) or horizontal (x= ). Plug in the value for x (or y) into the other equation and solve. Write your answer as an ordered pair.Example One x = 8 y = 3x - 3Example Two3x - 10y = -80 y = 5Example Three y = 2 x - 6y = 0Algebra One: Unit Five ~ System of Equations desotocountyschools.org/shs Maggie Dennis & Karen Hatch GOLD 13Lesson 19 Solving Systems by SubstitutionDOK 1 Write each answer as an ordered pair. 1. x = 4 2. y = -3 4x – 3y = 25 4x – 3y = 253. –x + 2y = 0 4. –x + 2y = 0 y = 7 x = 05. 4x – y = 9 6. 4x – y = 9 y = 3 y = -37. -2y – 5x = 17 8. -2y – 5x = 17 x = 1 y = -69. y = 0 10. x = 0 19x – y = 19 19x – y = 19Algebra One: Unit Five ~ System of Equations desotocountyschools.org/shs Maggie Dennis & Karen Hatch GOLD 14Lesson 20 Solving Systems of Equations Elimination NotesExample One Solve the following system: -x + y = 5 x + 2y = -2Example TwoSolve the following system: 3x + y = -2 -6x - 2y = 4Example Three Solve the following system: -7x + y = 1 3 - 3y = 7xAlgebra One: Unit Five ~ System of Equations desotocountyschools.org/shs Maggie Dennis & Karen Hatch GOLD 15Example Four Solve the following system: -x + y = 5 -3x + 3y = -2Example Five Solve the following system: 9x – 8y = 64 5x + 2y = 42Algebra One: Unit Five ~ System of Equations desotocountyschools.org/shs Maggie Dennis & Karen Hatch GOLD 16Lesson 20 Solving Systems of Equations EliminationDOK 1 Determine if the ordered pair is a solution of the given system. 1. (-4, 2) 4x – 3y = -22 2. (3, -7) x – 5y = 38 2x + y = -6 3x + 4y = -203. (-2, 3) 7y = 2x + 25 4. (5, 1) 3y = 4x – 17 3x = 16 – 2y 2x + y = 11DOK 2 5. At the Burger Palace, 2 hamburgers and 1 small order of fries cost $6.09. The Clarkes ordered 5 hamburgers and 5 small orders of fries and paid $17.95. What was the cost of 1 small order of fries?6. In Cleo’s class, g, the number of girls, is 3 times b, the number of boys. There are a total of 28 students in the class. Write a system of equations could be used to evaluate this situation to determine the number of boys in Cleo’s class. 7. Greg is going to solve the system of linear equations below. First Equation: 8x - 2 y = 8 Second Equation: 3x + 3 y = 9 Which of the following would Greg NOT use to solve this system of equations? A Solve the second equation for y and then substitute the result into the first equation. B Multiply the first and second equation by -6 to eliminate the y variable. C Solve the first equation for y and then substitute the result into the second equation. D Multiply the first equation by 3 and the second equation by 2 to eliminate the y variable.Algebra One: Unit Five ~ System of Equations desotocountyschools.org/shs Maggie Dennis & Karen Hatch

Lesson 15 Linear Equations

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