To solve by elimination, let say
#"Equation 1"# is #" "x-3y=0#
and
#"Equation 2"# is #" "3y-6=2x#
Now , to eliminate #y# you would wanna add Equation 1and Equation 2.
To do that you have to add the Left hand Side(#"LHS"#)of each equation.
Then you equate that to the sum of the Right Hand Sides(#"RHS"#) of the two equations.
If you do that correctly then,
#"LHS"=x-3y+3y-6=x-6#
Now, that's how you eliminated #y#
#"RHS"=0+2x=2x#
Now, do #"LHS"="RHS"#
#=>x-6=2x#
#=>-2x+x-6=2x-2x#
#=>-x-6=0#
#=>-x-6+6=6#
#=>-x=6#
#-1xx-x=-1xx6#
#=>color(blue)(x=-6)#
Now, to obtain #y# we want to eliminate #x#
#"Equation 1"# is #" "x-3y=0#
#"Equation 2"# is #" "3y-6=2x#
Multiply both side of #"Equation 1"# by #2# then add the resulting equation with #"Equation 2"#
#"Equation 1"# becomes #2x-6y=0#
Then with #"Equation 2"#
#=>"LHS"=2x-6y+3y-6=2x-3y-6#
#=>"RHS"=0+2x=2x#
Now , #"RHS"="LHS"#
#=>2x-3y-6=2x#
#=>-2x+2x-3y-6=2x-2x#
#=>-3y-6=0#
#=>-3y-6+6=0+6#
#=>(-3y)/(-3)=6/-3#
#=>color(blue)(y=-2)#
