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Answer 1 · 2018-01-26T10:53:23

the two graphs do not intersect

#4x^2+9y^2=1#

#4x^2+y^2=4#

subtract the two eqns

#8y^2=-3#

this leads to square root of a negative number

#:.#the graphs do not intersect, as is shown by their graphs below

graph{(4x^2+9y^2-1)(4x^2+y^2-4)=0 [-10, 10, -5, 5]}