# 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

### 1 個解答

• 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.