Step 1) Solve the first equation for #y#:
#2x + y = 5#
#2x - color(red)(2x) + y = 5 - color(red)(2x)#
#0 + y = 5 - 2x#
#y = 5 - 2x#
Step 2) Substitute #5 - 2x# for #y# in the second equation and solve for #x#:
#2x - 5y = 1# becomes:
#2x - 5(5 - 2x) = 1#
#2x - 25 + 10x = 1#
#12x - 25 = 1#
#12x - 25 + color(red)(25) = 1 + color(red)(25)#
#12x - 0 = 26#
#12x = 26#
#(12x)/color(red)(12) = 26/color(red)(12)#
#(color(red)(cancel(color(black)(12)))x)/cancel(color(red)(12)) = 13/6#
#x = 13/6#
Step 3) Substitute #13/6# for #x# in the solution to the first equation at the end of Step 1 and calculate #y#:
#y = 5 - 2x# becomes:
#y = 5 - (2 xx 13/6)#
#y = 5 - 26/6#
#y = (6/6 xx 5) - 26/6#
#y = 30/6 - 26/6#
#y = 4/6#
#y = 2/3#
The solution is #x = 13/6# and #y = 2/3# or #(13/6, 2/3)#
