#6x-2y=-3#, multiplying this equation by #3#
#18x-color(blue)(6y)=-9#.....equation #(1)#
#5x+3y=4#, multiplying this equation by#2#
#10x+color(blue)(6y)=8#.......equation #(2)#
Solving by elimination.
Adding equation #1# and #2# to eliminate #color(blue)(6y#
#18x-cancelcolor(blue)(6y)=-9#
#10x+cancelcolor(blue)(6y)=8#
#28x=-1#
#color(blue)(x=-1/28#
Finding #y# by substituting #x# in equation #1#
#18x-6y=-9#
#18x +9=6y#
#18*(-1/28) +9=6y#
#-9/14 +9=6y#
#(-9 +126)/9=6y#
#(117)/9=6y#
#13=6y#
#color(blue)(y=13/6#