Presentation on theme: "Wicomico High School Mrs. J. Austin 2009-2010 Chapter 7 : System of Equations."— Presentation transcript:
Wicomico High School Mrs. J. Austin Chapter 7 : System of Equations
Systems of Linear Equations Two linear equations graphed on the SAME coordinate plane. What are the THREE things that could happen? They could CROSS or INTERSECT They could NEVER CROSS or be PARALLEL They could be ON TOP OF EACH OTHER or COINCIDE
Solving a System of Linear Equations By Solving a System of Linear Equations, we are asking: Are there any Values for x and y that will “satisfy” or make BOTH equations TRUE? Is there a POINT that will make BOTH equations TRUE? What is the POINT OF INTERSECTION of these two lines? Find the values for x and y that will make BOTH equations TRUE.
Solving a System By Graphing 7.1 Transform each equation to Slope-Intercept Form For EACH of the TWO equations: PLOT the y – intercept, b COUNT, rise over run using the Slope, m. DRAW the straight line.
Solving a System By Graphing 7.1 Transform each equation into Slope-Intercept Form.
Solving a System By Substitution 7.2 Transitive Property A variable can be REPLACED with its equivalent. If two equations equal the SAME thing, they must then EQUAL each other. AND THEN The two equations are SET equal to each other
Solving a System By Substitution EXAMPLE: Now we know y=2. Substitute this into an equations to find x. Solve the first equation for x. Substitute the expression in for x in the second equation. Now SOLVE for y.
Solving a System By Elimination 7.3 Transitive Property Replace a variable with its equivalent. Set two expressions equal to each other, when they BOTH equal the same thing! Property of Equality Add or Subtract two equations to create a new equivalent equation. Transform the look of an equation by multiplication.
Solving a System By Elimination 7.3 Using Addition: ___________ Write the equations one above the other. Be sure the variables are lined up. Draw a line under them. Combine the Like-Terms to create a NEW equation. Solve for the variable. Substitute your answer into one of the equations to find the other variable.
Solving a System By Elimination 7.3 Using Subtraction _____________ Write the equations one above the other. Be sure the variables are lined up. Draw a line under them. Subtract the Like-Terms to create a NEW equation. Solve for the variable. Substitute your answer into one of the equations to find the other variable.
Solving a System By Elimination 7.4 Using Multiplication Before Adding or Subtracting: ___________________ __________________ Write the equations one above the other. Be sure the variables are lined up. Multiply the top equation by 4. Multiply the lower equation by 7. Draw a line under them. Distribute through each equation. Combine or Subtract the Like- Terms to create a NEW equation.
Solving a System By Elimination 7.4 Using Multiplication Before Adding or Subtracting. What would you MULTIPLY by? Multiply the top equation by 3. Solve the System using Subtraction: ____________________ The solution is the Point of Intersection: Solve this System. Start by multiplying the top equation by 2. Then add the two equations together eliminating the x terms. Solve for y. Substitute in the y value and solve for x. The solution is:
Special Types of Systems 7.5 One Solution: Lines Intersect at one point. Lines have different slopes. Lines may be PERPENDICULAR if they cross at 90⁰ angles. No Solution: Lines do not intersect. Lines have the SAME slope and DIFFERENT y-intercepts. Lines are PARALLEL. Many Solutions: Lines touch on every point. Lines have the SAME slope and SAME y-intercepts. Line COINCIDE.
Special Types of Systems 7.5 How Many Solutions Does the System Have?. System: Answer Choices: One Intersecting Lines None Parallel Lines Many Coinciding Lines
Writing and Solving Systems Slope –Intercept Form: Total Cost scenarios with given rates of change. The movie theater charges $8 per a ticket for its general customers. It offers a movie club discount of $5 per ticket if you join the club for a one-time fee of $15. How many movies would you have to go see to make joining the club beneficial? Write a system. Let x = the number of movie tickets y = total cost
Writing and Solving Systems Standard or General Form: Two different Items are given. At a grocery store, a customer pays a total of $9.70 for 1.8 pounds of potato salad and 1.4 pounds of coleslaw. Another customer pays a total of $6.55 for 1 pound of potato salad and 1.2 pounds of coleslaw. How much do 2 pounds of potato salad and 2 pounds of coleslaw cost? Write the system. Let: x = cost of potato salad y = cost of coleslaw.
Writing and Solving Systems High School Assessment Practice Questions: READ the question ALL the way through. RE-READ and define the variables. RE-READ and WRITE two equations to model the scenario. DECIDE which METHOD you will use to solve the System of Equations. SOLVE the System. RE-READ the question. Use YOUR SOLUTION to CONSTRUCT a written ANSWER to the question.
Solving Systems of Linear Inequalities 7.6 Graphing Linear Inequalities: Graph the first line. Shade the area defined by the first line. Graph the second line. Shade the area defined by the second line. The SOLUTUION to the System of Linear Inequalities is the AREA OF INTERSECTION. Re-shade the section of the graph that has been shaded by both of the equations.
Chp 7 Review Two linear functions graphed on a coordinate plane. They could CROSS, INTERSECT They could NEVER CROSS, PARALLEL They could be ON TOP OF EACH OTHER, COINCIDE Solving a System By Graphing 7.1 Solving a System By Substitution 7.2 Solving a System By Elimination 7.3 Identifying the Point of Intersection Testing a Solution to a System of Equations Special Types of Systems Writing and Solving Systems of Equations