show that the equation x^2+2xy+y^2+x+y-2=0 rebresent two paralil lines and find the equations of thos lines

Answer 1

x^2+2xy+y^2+x+y-2=0

Decomposition:

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

Expresion has zeros when:

x+y-1=0

and

(x+y+2)=0

x+y-1=0

y= -x+1

x+y+2=0

y= -x-2

Equation of sraight line:

y = mx + b

m=slope

b=y-intercept

y= -x+1 Slope -1

y= -x-2 Slope -1

Lines with the same slope are parallel.