Math 587 Assignment 2
John Doe
March 3, 2009

  1. At what point does the line 2x − y = 3 intersect the line x + 2y = −1?1

    Solution. The point of intersection may be obtained by solving the two equations simultaneously. For this multiply the first equation by 2 and add that to the second equation obtaining the equation

    5x = 5.

    Thus, x = 1, and, using either of the two original equations, one finds y = −1. The required point is (1,−1).

  2. Find all solutions of the quadratic equation x2 − x − 12 = 0.

    Solution. The well known formula for solution of the quadratic equation

    ax2 + bx + c = 0

    		(1)

    is

    x = − b ±b2 − 4ac 2a .

    		(2)

    In this case one finds

    x = 1 ±1 − 4(1)(−12) 2 (3) = 1 ± 7 2 (4) = 4 or − 3. (5)