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\nSolving a system of equations using RowReduce?
\nI'd like to determine the value of $\\alpha$ that minimizes $g(x, y, \\alpha) = -x^3 + 2x^2y - 3xy^2 + y^3$.\nWolfram alpha is unable to solve this equation but I know that the equations simplify to $x = 3y$ and $y = \\frac{1}{3}x$ so I tried to use a combination of RowReduce and Solve. My code is as follows:\nRowReduce[{x - y - 3y - 3x + y - x == 0, \n x - 3y + x - 3y - x + y == 0}, {x, y}, Integers]
\nI know this is a valid argument since it solves \n RowReduce[{x + y + 3y - 3x + y - x - y + y - x == 0, \n x + 3*y - x + y - x - y + y - x + y == 0}, {x, y}, Integers]
\nHowever, the command returns $\\alpha$ as being a complex number and not an integer. Any suggestions?\nThanks!\n\nA:\n\nHow about\nRowReduce[{x - y - 3*y - 3*x + y - x - y + y - x == 0, \n x - 3*y + x - 3*y - x + y == 0}, {x, y}, Integers] /. \n ComplexInfinity -> 0\n \n $\\left(\n \\begin{array}{cc}\n -1 & -3 \\\\\n -1 & -1 \\\\\n \\end{array}\n \\right)$\n \n A:\n \n A second attempt (and using the command-line solver)\n eqn2 = {x - y - 3*y - 3*x + y - x - y + y - x == 0, \n x - 3*y + x - 3*y - x + y == 0};\n \n s = Solve[eqn2, x] // ToRules // Evaluate\n \n (* {{y -> -\n 7582aa13b2\n \n https://documenter.getpostman.com/view/21882437/VUjEPVP6 https://documenter.getpostman.com/view/21883405/VUjEPVP8 https://documenter.getpostman.com/view/21861380/VUjEPVP7 https://documenter.getpostman.com/view/21885817/VUjEPVP9 https://documenter.getpostman.com/view/21828121/VUjEPVPB # Introduction\nWhat does your API do?
\nThings that the developers should know about
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