Investigating Linear Systems in Standard Form

[Remember: In Standard Form, slope = -(A/B) and y-intercept = C/B.]

Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now)
  1. Use the sliders and graph the equations to find and write the solution(s) of the following linear systems.
    a.) 4x + 2y = 8 and -2x + 5y = -4
    b.) -2x + 6y = 2 and -2x + 5y = 3
    c.) x - 3y = -4 and 9x + 3y = -6
    d.) 4x - 8y = 2 and 2x - 4y = -5
    e.) x - 3y = 2 and 3x - 9y = 6
  2. Look at the lines in 1c and find a geometric relationship between them. Now calculate the slopes of those graphs and write them in fraction form. Find and explain the relationship between the slopes in 1c.
  3. Calculate the slopes and y-intercepts in 1d. What is the relationship between the lines?
  4. Explain why there is only one line in 1e. What is the solution? Now calculate and compare the slopes and y-intercepts in 1e and explain the effects on the system.

EPankowski, 4/10/2007, Created with GeoGebra Updated by S.H. Lapinski

Please direct questions and comments to HCPS Mathematics Specialist Henrico County Public Schools, 2009