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Solving Systems by Graphing

Solving Systems by Graphing . Module IX, Lesson 1 Online Algebra 1 VHS@pwcs. What is a System of Equations?. A system of linear equations are two or more equations that may have a common solution. In Algebra 1, we can find the solution by: Graphing Substitution Elimination

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Solving Systems by Graphing

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  1. Solving Systems by Graphing Module IX, Lesson 1 Online Algebra 1 VHS@pwcs

  2. What is a System of Equations? • A system of linear equations are two or more equations that may have a common solution. • In Algebra 1, we can find the solution by: • Graphing • Substitution • Elimination • In this section we will concentrate on two equations and solve by graphing.

  3. Solutions to Systems • When two linear equations are solved, you will get one of the following: • One solution---an ordered pair • No solution • Infinite solutions

  4. Solving By Graphing • If you can’t remember how to graph a line, you need to spend some time reviewing unit 5. • When graphing the equations in a system, we can determine the solution by looking at the point of intersection of the two lines. • If they intersect in one point, the ordered pair that corresponds to that point is the solution. • If the lines never intersect, they are parallel and there is no solution for that system. • If the two equations graph the same line then the solution is all real numbers or an infinite number of solutions.

  5. Solving the Following System y = 2x – 3 y = x – 1 To the left are the graphs of the above lines. They intersect at the point (2, 1). Therefore the solution to the system is (2, 1)

  6. Try this one! Solve the following System: y = (1/2)x + 2 y = -3x – 3 Click to check your answer Your answer is where the lines intersect: (-2, 3)

  7. Graphing Calculators If you have a graphing calculator you may use this for some of your homework. The directions for the Texas Instrument follow this slide.

  8. y = 2x – 3 y = x – 1 Press the Y = button Enter the first equation, 2x – 3 ( the y = is already there for you) the x key is next to the ALPHA key Enter the second equation, x – 1 Press the GRAPH button. This should graph both lines. Press the 2nd key, then the TRACE (This is the CALC menu) We want to find the intersection, so either press the number 5 key or arrow down to intersection and press enter It will ask you three questions…first curve, second curve and guess. Just press enter for each If you did everything correct you will get x = 2 and y = 1. The solution. Using the Graphing CalculatorDirections for the TI

  9. If this didn’t work for the TI You need to put the calculator in “stage left”. This means in the following menus everything should be highlighted on the left. If they aren’t, arrow down and press enter on the left most option. The menus are MODE FORMAT (2nd Zoom)

  10. Using the Graphing CalculatorDirections for the Casio • Go to the graph menu. • Enter the first equation 2x – 3 (the y= is already entered for you) • The x key is under the ALPHA key • Enter the second equation x – 1. • Press DRAW (F6), this will graph both equations. If you don’t see the graph, check the window setting. • Press G-Solve (F5) • Press ISCT (F5), if you don’t see ISCT over the F5 Button push F6 for more options. • This should give you the solution x = 2, y = 1 y = 2x – 3 y = x – 1

  11. If this didn’t work for the CASIO • Go to SHIFT SET UP (over the menu button) • Arrow down and make sure that • Coord is on. • Grid is off • Axes are on • Label off

  12. Parallel Lines • If the two lines are parallel, you should be able to see this visually. They will not intersect and there will be no solution to the system. • If you ask the TI for the intersection it will give you a error message • If you ask the CASIO it will say not found. • There is no solution to the system when the lines are parallel.

  13. Same Line • If the lines are the same, you will only see one line. • IF you ask either calculator for the intersection, you will get coordinates. • BE CAREFUL! Your solution is actually all real numbers. • If the equations graph as one line, then there are an infinite number of solutions.

  14. y = 2x + 1 y = 3x -1 Try these! Click for the answers! (2, 5) (6, -1)

  15. Try these. • y = 3x – 4 y = -x + 4 2y = 6x – 8 y = -x + 1 These two equations These two graph as the same line. are parallel. There are infinite There are no solutions. solutions.

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