Step 1) Solve the second equation for #y)#
#-6x + y = 38#
#color(red)(6x) - 6x + y = color(red)(6x) + 38#
#0 + y = 6x + 38#
#y = 6x + 38#
Step 2) Substitute #6x + 38# for #y# in the first equation and solve for #x#:
#8x + 5y = -38# becomes:
#8x + 5(6x + 38) = -38#
#8x + (5 * 6x) + (5 * 38) = -38#
#8x + 30x + 190 = -38#
#(8 + 30)x + 190 = -38#
#38x + 190 = -38#
#38x + 190 - color(red)(190) = -38 - color(red)(190)#
#38x + 0 = -228#
#38x = -228#
#(38x)/color(red)(38) = -228/color(red)(38)#
#(color(red)(cancel(color(black)(38)))x)/cancel(color(red)(38)) = -6#
#x = -6#
Step 3) Substitute #-6# for #x# in the solution to the second equation at the end of Step 1 and calculate #y#:
#y = 6x + 38# becomes:
#y = (6 xx -6) + 38#
#y = -36 + 38#
#y = 2#
The solution is: #x = -6# and #y = 2# or #(-6, 2)#