The centroid of the triangle formed by the lines $x + 3y = 10$ and $6x^2 + xy - y^2 = 0$ is
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Remember that a homogeneous quadratic equation in $x$ and $y$ of the form $Ax^2 + Bxy + Cy^2 = 0$ represents a pair of straight lines passing through the origin. To find the centroid, first find the vertices by solving the line equations in pairs.