Step 1) Solve the first equation for #y#:
#2x + y = 5#
#-color(red)(2x) + 2x + y = -color(red)(2x) + 5#
#0 + y = -2x + 5#
#y = -2x + 5#
Step 2) Substitute #(-2x + 5)# for #y# in the second equation and solve for #x#:
#-29 = 5y - 3x# becomes:
#-29 = 5(-2x + 5) - 3x#
#-29 = (5 xx -2x) + (5 xx 5) - 3x#
#-29 = -10x + 25 - 3x#
#-29 = -10x - 3x + 25#
#-29 = (-10 - 3)x + 25#
#-29 = -13x + 25#
#-29 - color(red)(25) = -13x + 25 - color(red)(25)#
#-54 = -13x + 0#
#-54 = -13x#
#(-54)/color(red)(-13) = (-13x)/color(red)(-13)#
#54/13 = (color(red)(cancel(color(black)(-13)))x)/cancel(color(red)(-13))#
#54/13 = x#
#x = 54/13#
Step 3) Substitute #54/13# for #x# in the solution to the first equation at the end of Step 1 and calculate #y#:
#y = -2x + 5# becomes:
#y = (-2 xx 54/13) + 5#
#y = -108/13 + 5#
#y = -108/13 + (13/13 xx 5)#
#y = -108/13 + 65/13#
#y = -43/13#
The Solution Is: #x = 54/13# and #y = -43/13# or #(54/13, -43/13)#
