Solving by elimination causes one unknown term to be removed from the system of equations at a time.

Given:

#3x+4y=18#

#2x-4y=-8 to# To eliminate the #y# term, add the two equations:

#5x=10; x=2#

To eliminate the #x# term, multiply the two equations so the x term is the same in each (in this system, the multipliers are #2 and 3#):

#2*3x+2*4y=2*18#

#3*2x-3*4y=3*(-8) to#

#6x+8y=36#

#6x-12y=-24 to# then subtract the second equation from the first:

#cancel(6x)+8y=36#

#cancel(-6x)-(-12y)=-(-24) to#

#20y=60; y=3#

To check, substitute the answers into either equation:

#2x-4y=-8 to#

#2*2-4*3=-8 to#

#4-12=-8#

#-8=-8#