Step 1) Solve the second equation for #y#:
#-3x - y = -6#
#-3x - y + color(red)(y) + color(blue)(6) = -6 + color(blue)(6) + color(red)(y)#
#-3x - 0 + color(blue)(6) = 0 + color(red)(y)#
#-3x + 6 = y#
#y = -3x + 6#
Step 2) Substitute #(-3x + 6)# for #y# in the first equation and solve for #x#:
#4x - 2y = 3# becomes:
#4x - 2(-3x + 6) = 3#
#4x - (2 xx -3x) - (2 xx 6) = 3#
#4x - (-6x) - 12 = 3#
#4x + 6x - 12 = 3#
#(4 + 6)x - 12 = 3#
#10x - 12 = 3#
#10x - 12 + color(red)(12) = 3 + color(red)(12)#
#10x - 0 = 15#
#10x = 15#
#(10x)/color(red)(10) = 15/color(red)(10)#
#(color(red)(cancel(color(black)(10)))x)/cancel(color(red)(10)) = 15/10#
#x = 3/2#
Step 3) Substitute #3/2# for #x# in the solution to the second equation at the end of Step 1 and calculate #y#:
#y = -3x + 6# becomes:
#y = (-3 xx 3/2) + 6#
#y = (-9)/2 + 6#
#y = (-9)/2 + (2/2 xx 6)#
#y = (-9)/2 + 12/2#
#y = (-9 + 12)/2#
#y = 3/2#
The Solution Is:
#x = 3/2# and #y = 3/2#
Or
#(3/2, 3/2)#