Step 1) Solve the first equation for #x#:
#2x + 4y = 1#
#2x + 4y - color(red)(4y) = 1 - color(red)(4y)#
#2x + 0 = 1 - 4y#
#2x = 1 - 4y#
#(2x)/color(red)(2) = (1 - 4y)/color(red)(2)#
#x = 1/color(red)(2) - (4y)/color(red)(2)#
#x = 1/2 - 2y#
Step 2) Substitute #(1/2 - 2y)# for #x# in the second equation and solve for #y#:
#3x - 5y = 7# becomes:
#3(1/2 - 2y) - 5y = 7#
#(3 xx 1/2) - (3 xx 2y) - 5y = 7#
#3/2 - 6y - 5y = 7#
#3/2 - 11y = 7#
#3/2 - color(red)(3/2) - 11y = 7 - color(red)(3/2)#
#0 - 11y = (2/2 xx 7) - color(red)(3/2)#
#-11y = 14/2 - color(red)(3/2)#
#-11y = (14 - color(red)(3))/2#
#-11y = 11/2#
#-11y xx color(red)(-1/11) = 11/2 xx color(red)(-1/11)#
#(-11)/color(red)(-11)y = color(red)(cancel(color(black)(11)))/2 xx color(red)(-1/color(black)(cancel(color(red)(11))))#
#y = -1/2#
Step 3) Substitute #-1/2# for #y# in the solution to the first equation at the end of Step 1 and calculate #x#:
#x = 1/2 - 2y# becomes:
#x = 1/2 - (2 xx -1/2)#
#x = 1/2 - (-2/2)#
#x = 1/2 + 2/2#
#x = (1 + 2)/2#
#x = 3/2#
The Solution Is:
#x = 3/2# and #y = -1/2#
Or
#(3/2, -1/2)#
