# Systems of Linear Equations

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 effects do the top and bottom slider have on the graph of equation 1?

What relationship does the red graph have to equation 1?

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?

If you answered yes above, where do you find the solution(s) that work for both equations on the graph?

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?