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8.1 Solving Systems Graphically.notebook
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February 02, 2016
Mar 2319:37
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Chapter 8 8.1 Solving Systems of Equations
Graphically
• modelling a situation using a system of linearquadratic or quadraticquadratic equations• determining the solution of a system of linearquadratic or quadraticquadratic equations graphically• interpreting points of intersection and the number of solutions of a system of linearquadratic or quadraticquadratic equations• solving a problem that involves a system of linearquadratic or quadraticquadratic equations
Link the ideas
8.1 Solving Systems Graphically.notebook
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February 02, 2016
Apr 131:23 PM
Determine the number of solutions in each scenario. Drag the number of solutions to the box below each scenario.
Chapter
8LinearQuadratic Systems
no solutionone solution two solutions
two solutions
Apr 131:23 PM
Chapter
8QuadraticQuadratic Systems
no solutionone solution two solutions
Determine the number of solutions in each scenario.Drag the number of solutions to the box below each scenario.
8.1 Solving Systems Graphically.notebook
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February 02, 2016
Apr 131:23 PM
Solve the following system of equations graphically.
Chapter
8LinearQuadratic Systems
Drag the graphs of the given equations to locate them in the correct position on the grid. Determine the points of intersection to solve the system.
Verify the solutions by substituting into the original equations using the pen tool.
Apr 131:23 PM
Solve the following system of equations graphically
Chapter
8QuadraticQuadratic Systems
Drag the graphs of the given equations to locate them in the correct position on the grid. Determine the points of intersection to solve the system.
Verify the solutions by substituting into the original equations using the pen tool.
8.1 Solving Systems Graphically.notebook
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February 02, 2016
Apr 131:23 PM
Solve the system of equations graphically.
Chapter
8LinearQuadratic Systems
Use the pen tool to sketch the graphs of the equations.
Solve the following system of equations graphically
Chapter
8QuadraticQuadratic Systems
Use the pen tool to sketch the graph of the equations.
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From the graph, the points of intersectionare (0, 3) and (–2, –5).
8.1Example 2
1 a) Graph the corresponding functions. Adjust the dimensions of the graph so that the points of intersection are visible. Then, use the intersection feature.
Solve a System of LinearQuadratic Equations Graphicallya) Solve the following system of equations graphically: 4x – y + 3 = 0 2x2 + 8x – y + 3 = 0b) Verify your solution.
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8.1
Example 2: Your TurnSolve the system graphically and verify your solution.x – y + 1 = 0x2 – 6x + y + 3 = 0
Answer
8.1 Solving Systems Graphically.notebook
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Left Side Right Side Left Side Right Side 2x2 – 16x – y –35 2x2 – 8x – y –11= 2(3)2 – 16(3) – 5 = 2(3)2 – 8(3) – 5= 18 – 48 – 5 = 18 – 24 – 5 = –35 = –11 Left Side = Right Side Left Side = Right Side
b) Verify the solution (3, 5).
8.1Example 3
1 Graph the corresponding functions for both equations on the same coordinate grid.From the graph, the point of intersection is (3, 5).
a)
Solve a System of QuadraticQuadratic Equations Graphicallya) Solve: 2x2 – 16x – y = –35 2x2 – 8x – y = –11b) Verify your solution.
Since the ordered pair (3, 5) satisfies both equations, it is the solutionto the system.
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8.1
Example 3: Your TurnSolve the system graphically and verify your solution.2x2 + 16x + y = –26x2 + 8x – y = –19
Answer
8.1 Solving Systems Graphically.notebook
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Key ideas