How do you solve the following system: #2x-4y=6 , 3x - 3y = 2 #?

Question

2749 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-07-18T09:11:57

#x=-5/3# and #y=-7/3#

Dividing by #2#, #2x-4y=6# gives us #x-2y=3#

or #x-y-y=3#

Multiplying by #3#, we get

#3x-3y-3y=9#, but #3x-3y=2#,

therefore #2-3y=9#

or #2-9=3y# i.e. #3y=-7# and #y=-7/3#

Hence #x-2y=3# becomes #x-(-14/3)=3#

or #x=3-14/3=-5/3#

Hence #x=-5/3# and #y=-7/3#

Answer 2 · 2018-07-18T09:19:20

The solution is #S={(x=-5/3),(y=-7/3):}#

Solve the simutaneous equations by substitution

#{(2x-4y=6),(3x-3y=2):}#

#<=>#, #{(2x=4y+6),(3x-3y=2):}#

#<=>#, #{(x=2y+3),(3(2y+3)-3y=2):}#

#<=>#, #{(x=2y+3),(6y+9-3y=2):}#

#<=>#, #{(x=2y+3),(3y=-9+2):}#

#<=>#, #{(x=2*(-7/3)+3),(y=-7/3):}#

#<=>#, #{(x=-5/3),(y=-7/3):}#