Exercises

Follow the instructions with each exercise to solve simple linear systems

  1. 3a+2b=1.7
    a+3b=1.5

    The first equation minus three times the second equation yields

    Therefore plugging b into either equation yields a=.3

  2. 4.1a-3b=-6.41
    2a+9b=17.8

    Adding three times the first equation to the second equation yields
    Plugging into either equation yields the other solution: b=2

  3. During a late evening study session Will, Steve, and Megan all consume numerous caffeinated beverages to stay awake. Will drank a Red Bull, two cups of coffee, and a glass and a half of green tea. Steve drank 1.2 Red Bulls, 1 cup of coffee, and .5 cups of green tea. Megan on the otherhand drank 2.1 Red Bulls, 0.7 cups of coffee, and 2 Green Teas. Based on the effects of the drinks the three concluded Will consumed 490 mg of caffeine, Steve 286 mg, and Megan 400mg. Use a linear systems to solve for the amount of caffeine per beverage for the three types of drinks.

    Solution