SOLUTION: please help! why do intersecting lines represent a unique solution? give examples to support your answer.

Question 144314: please help!
why do intersecting lines represent a unique solution? give examples to support your answer.
Answer by shahid(44) (Show Source): You can put this solution on YOUR website!
it is a well known postulate that two lines always meet at only one point.there can not be more than one point where two lines can intersect.
Now consider the following system of linear equations
a*x+b*y=c ......(1)
g*x+f*y=d ........(2)
let they both intersect at two distinct points say (x1,y1) and (x2,y2)
then we will have
a*x1+b*y1=c a*x2+b*y2=c
g*x1+f*y1=d and g*x2+f*y2=d
so a*x1+b*y1=a*x2+b*y2 :::> a*(x1-x2)=b*(y2-y1)
similarly from others g*(x1-x2)=f*(y2-y1)
by dividing these equations we get a/g=b/f which can not be possible because lines are not parallel according to our supposition.hence
x1-x2=0 and y2-y1=0
x1=x2 and y1=y2
which prove that points are not distinct .
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