Step 1) Solve the second equation for #x#:
#x + 3y = -5#
#x + 3y - color(red)(3y) = -5 - color(red)(3y)#
#x + 0 = -5 - 3y#
#x = -5 - 3y#
Step 2) Substitute #-5 - 3y# for #x# in the first equation and solve for #y#:
#3(-5 - 3y) - 2y = 7#
#-15 - 9y - 2y = 7#
#-15 - 11y = 7#
#color(red)(15) - 15 - 11y = color(red)(15) + 7#
#0 - 11y = 22#
#-11y = 22#
#(-11y)/color(red)(-11) = 22/color(red)(-11)#
#(color(red)(cancel(color(black)(-11)))y)/cancel(color(red)(-11)) = -2#
#y = -2#
Step 3) Substitute #-2# for #y# in the solution to the second equation at the end of Step 1 and calculate #x#:
#x = -5 - (3 xx -2)#
#x = -5 - (-6)#
#x = -5 + 6#
#x = 1#
The solution is #x = 1# and #y = -2#