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 xy : 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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 Winter '10
 golishr

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