Step 1) Solve the second equation for #y#:
#y + 4x = 16#
#y + 4x - color(red)(4x) = 16 - color(red)(4x)#
#y + 0 = 16 - 4x#
#y = 16 - 4x#
Step 2) Substitute #(16 - 4x)# for #y# in the first equation and solve for #x#:
#2x - 4y = 6# becomes:
#2x - 4(16 - 4x) = 6#
#2x - (4 * 16) + (4 * 4x) = 6#
#2x - 64 + 16x = 6#
#2x + 16x - 64 = 6#
#(2 + 16)x - 64 + color(red)(64) = 6 + color(red)(64)#
#18x - 0 = 70#
#18x = 70#
#(18x)/color(red)(18) = 70/color(red)(18)#
#x = 35/9#
Step 3) Substitute #35/9# for #x# in the solution to the second equation at the end of Step 1 and calculate #y#:
#y = 16 - 4x# becomes:
#y = 16 - (4 xx 35/9)#
#y = 144/9 - 140/9#
#y = (144 - 140)/9#
#y = 4/9#
The Solution Is:
#x = 35/9# and #y = 4/9#
Or
#(35/9, 4/9)#
