At what point does the line 2 x - 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
| 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 ax^{2} + b x + c = 0 is
| x = {-b ± SQRT{b^{2} - 4ac}}/{2a} . |
In this case one finds
| x = {1 ± SQRT{1 -4(1)(-12)}}/{2} = {1 ± 7}/{2} = 4 or -3 . |