Systems of Linear Equations

Use the interactive applet below to help answer the following questions.

Show graph 1 in red and play with some of the red sliders and buttons on the right side of the screen. What effect does changing the top slider have on the equation?

What effect does the bottom slider have on the equation?

What relationship does the red graph have to equation 1?

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Set equation 1 to y = 2x-5 and equation 2 to y = -x+7. If the red graph represents all of the solutions to equation 1 and the blue graph all the solutions of equation 2, is there a solution that works for both equations? How many solutions are there?

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If you answered yes above, where do you find the solution and what are its coordinates?

Now Set equation 1 to y = 3x-2 and equation 2 to y = 3+5. How many solutions are there that work for both equations?

What can you say about the graphs of two linear equations that have no common solution?

Graph the equations y =12-5x and 2y+3x = -4. Simply type each equation into the input bar at the top left of the applet to graph each equation. Use the intersect tool in the point tool menu and click on the intersection to create a point where the graphs meet. Create a text box and tell me the solution to the system of equations.