a pair of straight line
y=3x
y= -x
then -3x^2-2xy+y^2=0 represent the above two lines,why???
why multiply both equation and state that it is a representation of two straight line??
thz
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- 1 十年前最愛解答
-3x^2-2xy+y^2=0 represent the above two lines
This sentense means -3x^2-2xy+y^2=0 can represent all the points in y = 3x and y = -x.
We have two equations :
y = 3x ------ 1
y = -x ------ 2
We aim to find an equation to represent the two equations above :
y - 3x = 0
y + x = 0
Multiplying two equations
(y - 3x)(y + x) = 0
thus we get -3x^2 -3xy + xy + y^2 = 0
finally : -3x^2-2xy+y^2=0
Thus -3x^2-2xy+y^2=0 represent the above two lines.
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