A box contains 6 plain pencils and 2 pens. A second box contains 3 color pencils and 5 crayons. One item from each box is chosen
at random. What is the probability that a pen from the first box and a crayon from the second box are selected? Write your answer as a fraction in simplest form.
y is definied as y = 3x - 1. Substitute 3x - 1 for y in xy = 9, obtaining:
x(3x - 1) = 9. Then:
3x^2 - x - 9 = 0. In this quadratic, the coefficients are a = 3, b = -1 and c = -9.
Calculating the discriminant b^2 - 4ac, we get (-1)^2 - 4(3)(-9), or 1 + 108, or 109. Because the discriminant is positive, we have two real, unequal roots.
