Question 409847: My teacher gave me the system of equations to solve symbolically for intersections x^2 + 4y^2 = 25, and x +2y = 7
I tried to solve it, but got stuck. The answer I eventually got was very different then the answer he gave me, which was (3,2) and (4, 1.5). He then refused to explain how he got that answer. Can you help explain how to do this problem correctly?
Answer by robertb(5830)   (Show Source):
You can put this solution on YOUR website! Square the linear equation, giving  . Subtract the equation  from the preceding equation, to get 4xy = 24, or xy = 6, or y = 6/x.
Then
<==> 
<==> 
<==> 
==> x = 4, -4, 3, -3
The graph of is an ellipse with vertices (-5,0) and (5,0); and co-vertices (0, 5/2) and (0, -5/2). The graph of x +2y = 7 is a line with slope -1/2 and y-intercept 7/2. The two graphs intersect only at two points (with both x-coordinates positive). Hence the intersection points are:
When x = 4, y = 6/4 = 3/2 ==> (4, 1.5).
When x = 3, y = 6/3 = 2 ==> (3,2).
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