Step 1) Solve the second equation for #x#:
#x + 4y = 1#
#x + 4y - color(red)(4y) = 1 - color(red)(4y)#
#x + 0 = 1 - 4y#
#x = 1 - 4y#
Step 2) Substitute #(1 - 4y)# for #x# in the first equation and solve for #y#:
#4y = -7x + 9# becomes:
#4y = -7(1 - 4y) + 9#
#4y = (-7 xx 1) + (-7 xx -4y) + 9#
#4y = -7 + 28y + 9#
#4y = -7 + 9 + 28y#
#4y = 2 + 28y#
#4y - color(red)(28y) = 2 + 28y - color(red)(28y)#
#(4 - color(red)(28))y = 2 + 0#
#-24y = 2#
#(-24y)/color(red)(-24) = 2/color(red)(-24)#
#(color(red)(cancel(color(black)(-24)))y)/cancel(color(red)(-24)) = -1/12#
#y = -1/12#
Step 3) Substitute #-1/12# for #y# in the solution to the second equation at the end of Step 1 and calculate #x#:
#x = 1 - 4y# becomes:
#x = 1 - (4 xx -1/12)#
#x = 1 - (-4/12)#
#x = 1 - (-1/3)#
#x = 1 + 1/3#
#x = 3/3 + 1/3#
#x = 4/3#
The Solution Is: #x = 4/3# and #y = -1/12# or #(4/3, -1/12)#
