SOLUTION: 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

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).

RELATED QUESTIONS
We are learning this in class and my teacher goes way to fast. Could you please help me... (answered by mananth)

Can someone help me solve the system of equations here symbolically, graphically and... (answered by unlockmath)

Solve the system of equations 2x-2y-2z=3,x+4y-z=2, and -2x-8y+2z=-4. I tried to plot it... (answered by Alan3354)

A circle contains the points (0,0), (-7,-17), and (18,-12). Solve a system of three... (answered by ankor@dixie-net.com)

Please help me solve this system of equations for all intersections. (4/x^2)+ (6/y^4) (answered by Alan3354)

SUBSTITUTION AND ELIMINATION 1. 2X+Y-3Z=0 2. -2X+2Y+Z=-7 3. X-4Y-3Z=7 TRYING TO... (answered by stanbon,MathLover1)

I know how to solve for X and Y in linear systems of equations using SUBSTITUTION. My... (answered by htmentor)

How would I solve this problem? Graph the equations of the system. Then solve the... (answered by ewatrrr)

I have to solve the system of equations which are 2x-4y+2z=16 -2x+5y+2z=-34 x-2y+2z=4 (answered by scott8148)