Step 1) Solve the second equation for #y#:
#-5x - y = 14#
#-5x - color(blue)(14) - y + color(red)(y) = 14 - color(blue)(14) + color(red)(y)#
#-5x - 14 - 0 = 0 + y#
#-5x - 14 = y#
#y = -5x - 14#
Step 2) Substitute #(-5x - 14)# for #y# in the first equation and solve for #x#:
#7y - 6x - 5 = 0# becomes:
#7(-5x - 14) - 6x - 5 = 0#
#-(7 xx 5x) - (7 xx 14) - 6x - 5 = 0#
#-35x - 98 - 6x - 5 = 0#
#-35x - 6x - 98 - 5 = 0#
#(-35 - 6)x - 103 = 0#
#-41x - 103 = 0#
#-41x - 103 + color(red)(103) = 0 + color(red)(103)#
#-41x - 0 = 103#
#-41x = 103#
#(-41x)/color(red)(-41) = 103/color(red)(-41)#
#(-color(red)(cancel(color(black)(41)))x)/cancel(color(red)(-41)) = -103/41#
#x = -103/41#
Step 3) Substitute #-103/41# for #x# in the solution to the second equation at the end of Step 1 and calculate #y#:
#y = -5x - 14# becomes:
#y = (-5 xx -103/41) - 14#
#y = 515/41 - (41/41 xx 14)#
#y = 515/41 - 574/41#
#y = -59/41#
The Solution Is:
#x = -103/41# and #y = -59/41#
Or
#(-103/41, -59/41)#
