Chapter 9 Quadratic Relations and Conic Sections - 9.7 Solve Quadratic Systems - 9.7 Exercises - Skill Practice - Page 662: 36

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Multiplying the first equation by $16$ we get: $8x^2+4y^2=16\\4y^2=16-8x^2$ Thus the two equations are basically the same, and we have infinitely many solutions. The solutions can be obtained by (for any $x$: $y=\sqrt{4-2x^2}$