Three straight lines are defined by three equations x y 0

Three straight lines are defined by three equations: x + y = 0 x-y = 0 2x + y = 1 The three lines form a triangle with vertices at (0,0), (1/3, 1/3), (1, -1) (0,0),(2/3, 2/3).(1,-1) (1,1), (1, -1),(2,1) (1,1),(3, -3) (-2, 1)

Solution

s0lving

x+y=0

x-y=0

x+y+x-y=0+0

2x =0

x=0

x-y=0

=>0-y=0

=>y=0

point of intersection is (0,0)

s0lving

2x+y=1

x-y=0

2x+y+x-y=1+0

3x =1

x=1/3

x-y=0

=>1/3 -y=0

=>y=1/3

point of intersection is (1/3,1/3)

s0lving

2x+y=1

x+y=0

2x+y-(x+y)=1-0

x =1

x+y=0

=>1+y=0

=>y=-1

point of intersection is (1,-1)

vertices are (0,0,)(1/3,1/3),(1,-1)