MODERATE EXERCISES

(4)

 Sketch the following systems and find any real solutions:

 (a)  x2 + y2 = 25 and x2 - y2 = 7

 (b)  16x2 + 9y2 = 144 and y = x2 + 5

(a) 

From the graph, we see there is four solutions.  Using the elimination method:
  x2 + y2 = 25
+ x2 - y2 = 7
----------------
2x2 = 32
 x2 = 16
 x = 4

 (4)2 + y2 = 25
 16 + y2 = 25
  y2 = 9
  y = 3

The solutions are { (4,3), (4,-3), (-4,3), (-4,-3) }

(b) 

From the graph we see that there is no intersection and therefore no real solutions