# The combined equation of the lines passing through the origin and having slopes 3 and -2 is

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by wwlaxiShruti

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by wwlaxiShruti

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Since the lines are passing through the origin then (0,0) will be the points of both ,

equation of first line

y - 0 = 3(x-0)

y = 3x ----(1)

equation of second line ,

y = -2x -----(2)

combining(1) & (2 We get (y+2x)(2y-x) = 0)

We get 6x² - y² + xy = 0

equation of first line

y - 0 = 3(x-0)

y = 3x ----(1)

equation of second line ,

y = -2x -----(2)

combining(1) & (2 We get (y+2x)(2y-x) = 0)

We get 6x² - y² + xy = 0

(y-0) = 3(x-0)

⇒ y = 3x

⇒ y - 3x = 0 ---------(1)

equation of a line passing through origin(0,0) with slope -2 is

(y-0) = -2(x-0)

⇒ y = -2x

⇒ y + 2x = 0 ---------(2)

Combining lines (1) and (2), we get

(y - 3x)(y + 2x) = 0

⇒ y² + (2x-3x)y - 6x² = 0

⇒ y² - 6x² -xy = 0

⇒ 6x² - y² + xy = 0

Equation of combination of lines is