#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
