Question 579755
Find the coordinates of any points where the line 2x + 3y = 6 and the ellipse 4x^2 + 9y^2 = 36 intersect.
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2x+3y=6
3y=6-2x
y=2-2x/3
..
4x^2+9y^2=36
sub y in equation
4x^2+9(2-2x/3)^2=36
4x^2+9(4-8x/3+4x^2/9)=36
4x^2+36-24x+4x^2=36
8x^2-24x=0
x^2-3x=0
x(x-3)=0
x=0
y=2-2x/3=2-0=2 
or
x=3
y=2-2x/3=2-6/3=2-2=0
..
ans:
Two points of intersection:(0,2) and (3,0)