Step 1) Solve the first equation for #x#:
#x + 2y = 1#
#x + 2y - color(red)(2y) = 1 - color(red)(2y)#
#x + 0 = 1 - 2y#
#x = 1 - 2y#
Step 2) Substitute #(1 - 2y)# for #x# in the second equation and solve for #y#:
#6x + 3y = 11# becomes:
#6(1 - 2y) + 3y = 11#
#(6 * 1) - (6 * 2y) + 3y = 11#
#6 - 12y + 3y = 11#
#6 + (-12 + 3)y = 11#
#6 + (-9)y = 11#
#6 - 9y = 11#
#6 - color(red)(6) - 9y = 11 - color(red)(6)#
#0 - 9y = 5#
#-9y = 5#
#(-9y)/color(red)(-9) = 5/color(red)(-9)#
#(color(red)(cancel(color(black)(-9)))y)/cancel(color(red)(-9)) = -5/9#
#y = -5/9#
Step 3) Substitute #-5/9# for #y# in the solution to the first equation at the end of Step 1 and calculate #x#:
#x = 1 - 2y# becomes:
#x = 1 - (2 * -5/9)#
#x = 1 - (-10/9)#
#x = 1 + 10/9#
#x = 9/9 + 10/9#
#x = 19/9#
The Solution Is:
#x = 19/9# and #y = -5/9#
Or
#(19/9, -5/9)#
