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A straight lines L through the origin meets the lines x+y=1 and x+y=3 at P and Q respectively. Through P and Q two straight lines `L_1` and `L_2` are drawn, parallel to 2x-y=5 and 3x+y=5 respectively. Line `L_1` and `L_2` intersect at R. Show that the locus of R as L varies is a straight line.

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Locus of R is x-3y+5=0
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PATHFINDER-CARTESIAN COORDINATES AND STRAIGHT LINE-QUESTION BANK
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