Question 143454
Find the points of intersection of the graphs: 
x^2/4 + y^2/9 =1 
& y = -x-2
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Substitute to solve for "x":

[x^2/4] + [(-x-2)^2/9] = 1
[x^2/4] + [(x^2+4x+4)/9] = 1
9x^2 + 4x^2+16x+16 = 36
13x^2 + 16x - 20 = 0
(x+2)(13x-10) = 0
x = -2 or x = 10/13
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If x=-2, solve for Y:
(4/4)+ y^2/9 = 1
1 + y^2/9 = 1
y = 0
Point of intersection (-2,0)
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If x = 10/13, solve for y:
(10/13)^2/4 + y^2/9 = 1
y^2/9 = 0.85207...
y^2 = 7.668639...
y = - 2.76923
Points of intersection:  (10/13 , -2.76913...)
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Cheers,
Stan H.