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?

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 x^{2} − x − 12 = 0.

Solution. The well known formula for solution of the quadratic equation ax^{2} + bx + c = 0 is

x = \frac{−b ± \sqrt{b^{2} − 4ac}}{2a} .

In this case one finds

x = \frac{1 ± \sqrt{1 − 4(1)(−12)}}{2} = \frac{1 ± 7}{2} = 4 or − 3 .