+9466 2: Here's a graph: https://www.desmos.com/calculator/idxee4c2dz
The solution to the system is the part that is shaded by both red and blue.
(0, 4) is a solution to the system.
Check the point in both inequalitites to make sure it makes them both true.
4 ≥ \(-\frac12(0)+2\frac12\) ?
4 ≥ \(2\frac12\) True.
4 < \(\frac15(0)+6\) ?
4 < 6 True.
3: \(\Large{\frac{\frac{1}{x^2}+\frac{2}{y}}{\frac{5}{x}-\frac{6}{y^2}}}\)
\(\Large{=\,\frac{\frac{y}{x^2y}+\frac{2x^2}{x^2y}}{\frac{5y^2}{xy^2}-\frac{6x}{xy^2}} \\~\\ =\,\frac{\frac{y+2x^2}{x^2y}}{\frac{5y^2-6x}{xy^2}} \\~\\ =\,\frac{y+2x^2}{x^2y}\cdot\frac{xy^2}{5y^2-6x} \\~\\ =\,\frac{y+2x^2}{x}\cdot\frac{y}{5y^2-6x} \\~\\ =\,\frac{y^2+2x^2y}{5xy^2-6x^2}}\)
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