Untitled-111

# Untitled-111 - DEPENDENCE OF STRAIGHT LINES one of three...

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Unformatted text preview: DEPENDENCE OF STRAIGHT LINES one of three conditions: A B I CONCURRENT If A—1 at —B—1, i.e. the lines intersect at one point. 2 2 Example; Show that 3x+y = 12 and x-y : 8 have one set of solutions. . A1 3 Bl 1 . . . . Solution: Here — = —, ——— = —, there is one intersection pomt. A2 1 B2 ~1 To ﬁnd the interection: 3x+y = 12 x—y = 8 4x = 20 x = 5, y = —3 A B C II PARALLEL If ——1— : ——1— :t ——1—,i.e., the lines do not intersect. A2 B2 C 2 2 Example: Show that 2x+3y—6 = 0 and y = —§x~4 do not intersect. A1 2 5L —6 Solution: Here 1; = E and 82 = g at E, the lines are parallel. Alternatively: 2x+3y—6 = O is equivalent to 3y 2 —2x+6 2 2 — ———x+2 3’ y since m1 2 m2 = 3 then the lines are parallel. A B C III COINCIDENT If —1.= —1 —1, i.e., there is an inﬁnite A2 32 C2 number of solutions. Example; Show that y 2 295—4 and 4x—2y—8 : O are coincident. Solution: Here 2x—y—4 = 0 and 4x—2y—8 = 0 give g = {—21— : :—:, coincident. Ifwe change 4x—2y—8 = O to —2y 2 —4x+8 y = 2x—4 which is exactly the same as the 1st line. 2 lines coincide. ...
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