Math 587 Assignment 2

John Doe

March 3, 2009

At what point does the line $2 x - y = 3$ intersect the line $x + 2 y = - 1$ ?
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
$5 x = 5 .$
Thus, $x = 1$ , and, using either of the two original equations, one finds $y = - 1$ . The required point is $(1, - 1)$ .
Find all solutions of the quadratic equation $x^{2} - x - 12 = 0$ .
Solution. The well known formula for solution of the quadratic equation $a x^{2} + b x + c = 0$ is
$x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a} .$
In this case one finds
$x = \frac{1 \pm \sqrt{1 - 4 (1) (- 12)}}{2} = \frac{1 \pm 7}{2} = 4 or - 3 .$