Step 1) Solve the first equation for #x#:
#x - 3y = -1#
#x - 3y + color(red)(3y) = -1 + color(red)(3y)#
#x - 0 = -1 + 3y#
#x = -1 + 3y#
Step 2) Substitute #-1 + 3y# for #x# in the second equation and solve for #y#:
#7x + 15y = 32# becomes:
#7(-1 + 3y) + 15y = 32#
#(7 * -1) + (7 * 3y) + 15y = 32#
#-7 + 21y + 15y = 32#
#-7 + (21 + 15)y = 32#
#-7 + 36y = 32#
#color(red)(7) - 7 + 36y = color(red)(7) + 32#
#0 + 36y = 39#
#36y = 39#
#(36y)/color(red)(36) = 39/color(red)(36)#
#(color(red)(cancel(color(black)(36)))y)/cancel(color(red)(36)) = (13 xx 3)/color(red)(12 xx 3)#
#y = (13 xx color(red)(cancel(color(black)(3))))/color(red)(12 xx color(black)(cancel(color(red)(3))))#
#y = 13/12#
Step 3) Substitute #13/12# for #y# in the solution to the first equation at the end of Step 1 and calculate #x#:
#x = -1 + 3y# becomes:
#x = -1 + (3 * 13/12)#
#x = -1 + 39/12#
#x = (12/12 * -1) + 39/12#
#x = -12/12 + 39/12#
#x = 27/12#
#x = (3 xx 9)/(3 xx 4)#
#x = (color(red)(cancel(color(black)(3))) xx 9)/(color(red)(cancel(color(black)(3))) xx 4)#
#x = 9/4#
The solution is: #x = 9/4# and #y = 13/12# or #(9/4, 13/12)#
