Problema 2.17(a)

Decida si cada una de las siguientes ternas de rectas son o no concurrentes.[br](a) [math]x−y−1=0[/math], [math]x+y−3=0[/math] y [math]3x−y−5=0[/math].
Sol:
De acuerdo con el problema 2.12(a) son concurrentes, ya que[br][img]data:image/png;base64,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[/img][br]Si queremos encontrar el punto de concurrencia las tres rectas, basta encontrar el punto de concurrencia entre dos de ellas. Esto es, resolver el sistema de ecuaciones formado por las ecuaciones de dos de ellas.

Information: Problema 2.17(a)