Step 1) Solve the first equation for #x#:
#x + y = 40#
#x + y - color(red)(y) = 40 - color(red)(y)#
#x + 0 = 40 - y#
#x = 40 - y#
Step 2) Substitute #40 - y# for #x# in the second equation and solve for #y#:
#2x + .7y = 12# becomes:
#2(40 - y) + .7y = 12#
#80 - 2y + .7y = 12#
#80 - 1.3y = 12#
#-color(red)(80) + 80 - 1.3y = -color(red)(80) + 12#
#0 - 1.3y = -68#
#-1.3y = -68#
#(-1.3y)/color(red)(-1.3) = (-68)/color(red)(-1.3)#
#(color(red)(cancel(color(black)(-1.3)))y)/cancel(color(red)(-1.3) )= 52.308#
#y = 52.308# rounded to the nearest thousandth.
Step 3) Substitute #52.308# for #x# in the solution to the first equation at the end of Step 1 and calculate #x#:
#x = 40 - y# becomes:
#x = 40 - 52.308#
#x = -12.308#
The solution is: #x = -12.308# and #y = 52.308# or #(-12.308, 52.308)# rounded to the nearest thousandth.
