#color(white)(+)-4x+2y=-12#

#color(white)(+)#

#color(white)(+)color(white)(-)3x+2y=9#

We need to *eliminate* one of the variables. The #y#s are already equal, so we will subtract the two equations and remove #2y#:

#color(white)(+)-4x+cancel(2y)=-12#

#color(black)(-)#

#color(white)(+)color(white)(-)3x+cancel(2y)=color(white)(-)9#

...............................................................

#-7x=-21#

Now we just solve for #x#

#-7x=-21#

*Divide by #7# on both sides*

#x=(-21)/-7# or #x=3#

Now we have #x#; we need to find the value of #y#. To do that, we pick an equation and solve for #y#, substituting #x# for #3#.

#3x+2y=9#

#3(3)+y=9#

#9+y=9#

#9+y color(purple)(-9)=9color(purple)(-9)#

#y=0#

Just to double check our work, let's solve the second equation using both #x# and #y# as #3# and #0#, respectively.

#-4x+2y=-12#

#-4(3)+2(0)# should equal #-12#

#-12+0=-12#

We were right! Congratulations. Nice work.

Hope this is helpful