Step 1) Solve the first equation for #x#:
#x + 8y = 15#
#x + 8y - color(red)(8y) = 15 - color(red)(8y)#
#x + 0 = 15 - 8y#
#x = 15 - 8y#
Step 2) Substitute #(15 - 8y)# for #x# in the second equation and solve for #y#:
#5x - 7y = 12# becomes:
#5(15 - 8y) - 7y = 12#
#(5 xx 15) - (5 xx 8y) - 7y = 12#
#75 - 40y - 7y = 12#
#75 + (-40 - 7)y = 12#
#75 + (-47)y = 12#
#75 - 47y = 12#
#75 - color(red)(75) - 47y = 12 - color(red)(75)#
#0 - 47y = -63#
#-47y = -63#
#(-47y)/color(red)(-47) = -63/color(red)(-47)#
#y = 63/47#
Step 3) Substitute #63/47# for #y# in the solution to the first equation at the end of Step 1 and calculate #x#:
#x = 15 - 8y# becomes:
#x = 15 - (8 xx 63/47)#
#x = 15 - 504/47#
#x = (47/47 xx 15) - 504/47#
#x = 705/47 - 504/47#
#x = 201/47#
The Solution Is:
#x = 201/47# and #y = 63/47#
Or
#(201/47, 63/47)#
