Step 1) Solve the first equation for #x#:
#x + 8y = 3#
#x + 8y - color(red)(8y) = 3 - color(red)(8y)#
#x + 0 = 3 - 8y#
#x = 3 - 8y#
Step 2) Subsitute #3 - 8y# for #x# in the second equation and solve for #y#:
#4x + 5y = -2# becomes:
#4(3 - 8y) + 5y = -2#
#(4 * 3) - (4 * 8y) + 5y = -2#
#12 - 32y + 5y = -2#
#12 + (-32 + 5)y = -2#
#12 - 27y = -2#
#-color(red)(12) + 12 - 27y = -color(red)(12) - 2#
#0 - 27y = -14#
#-27y = -14#
#(-27y)/color(red)(-27) = (-14)/color(red)(-27)#
#(color(red)(cancel(color(black)(-27)))y)/cancel(color(red)(-27)) = 14/27#
#y = 14/27#
Step 3) Substitute #14/27# for #y# in the solution to the first equation at the end of Step 1 and calculate #x#:
#x = 3 - 8y# becomes:
#x = 3 - (8 * 14/27)#
#x = 3 - 112/27#
#x = (3 * 27/27) - 112/27#
#x = 81/27 - 112/27#
#x = -31/27#
The solution is: #x = -31/27# and #y = 14/27# or #(-31/27, 14/27)#
