Step 1) Solve the first equation for #y#:
#0.05x + 0.25y = 66#
#-color(red)(0.05x) + 0.05x + 0.25y = -color(red)(0.05x) + 66#
#0 + 0.25y = -0.05x + 66#
#0.25y = -0.05x + 66#
#color(red)(4) xx 0.25y = color(red)(4)(-0.05x + 66)#
#1y = (color(red)(4) xx -0.05x) + (color(red)(4) xx 66)#
#y = -0.2x + 264#
Step 2) Substitute #(-0.2x + 264)# for #y# in the second equation and solve for #x#:
#0.15x + 0.05y = 72# becomes:
#0.15x + 0.05(-0.2x + 264) = 72#
#0.15x + (0.05 xx -0.2x) + (0.05 xx 264) = 72#
#0.15x + (-0.01x) + 13.2 = 72#
#0.15x - 0.01x + 13.2 = 72#
#(0.15 - 0.01)x + 13.2 = 72#
#0.14x + 13.2 = 72#
#0.14x + 13.2 - color(red)(13.2) = 72 - color(red)(13.2)#
#0.14x + 0 = 58.8#
#0.14x = 58.8#
#(0.14x)/color(red)(0.14) = 58.8/color(red)(0.14)#
#(color(red)(cancel(color(black)(0.14)))x)/cancel(color(red)(0.14)) = 420#
#x = 420#
Step 3) Substitute #420# for #x# in the solution to the first equation at the end of Step 1 and calculate #y#:
#y = -0.2x + 264# becomes:
#y = (-0.2 xx 420) + 264#
#y = -84 + 264#
#y = 180#
The Solution Is: #x = 420# and #y = 180# or #(420, 180)#
