First, line up the equations as an addition problem:
___#x + 2y=13#
#+# #3x+2y=5#
As you can see, both equations have a #2y# in common, so this is what you need to eliminate in order to find the value of #x#. To do this, multiply the entire second equation by #-1#:
#(-1)# x #(3x+2y=5)# #-># #-3x-2y=-5#
Now, put the addition problem back together:
..........#x + 2y=13#
#+# #-3x-2y=-5#
________,
..........#-2x=8#
Now, divide each side by #-2# to isolate #x#:
#(-2x)/-2##=##8/-2# #-># #x=-4#
Since we know the value of #x# is #-4# now, we can substitute #-4# in for #x# in either equation. Let's use the first one:
#(-4) + 2y=13#
Add #4# to both sides of the equation to isolate #2y#:
#(-4)+ 2y=13#
#+4# ......................#+4#
______,
...................#2y=17#
Now, divide each side by #2# to isolate #y#:
#(2y)/2##=##17/2# #-># #y=8.5#
