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 $\left(1,-1\right)$.

2. Find all solutions of the quadratic equation $x^2-x-12=0$.

   Solution. The well known formula for solution of the quadratic equation $a{x}^2+bx+c=0$ is $$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}.$$ In this case one finds $$x=\frac{1\pm \sqrt{1-4\left(1\right)\left(-12\right)}}{2}=\frac{1\pm 7}{2}=4\mathrm{or}-3.$$