Step 1) Because the second equation is already solve for #y# we can substitute #(-4x + 6)# for #y# in the first equation and solve for #x#:
#6x + 2y = 11# becomes:
#6x + 2(-4x + 6) = 11#
#6x + (2 xx -4x) + (2 xx 6) = 11#
#6x + (-8x) + 12 = 11#
#6x - 8x + 12 = 11#
#(6 - 8)x + 12 = 11#
#-2x + 12 = 11#
#-2x + 12 - color(red)(12) = 11 - color(red)(12)#
#-2x + 0 = -1#
#-2x = -1#
#(-2x)/color(red)(-2) = (-1)/color(red)(-2)#
#(color(red)(cancel(color(black)(-2)))x)/cancel(color(red)(-2)) = 1/2#
#x = 1/2#
Step 2) Substitute #1/2# for #x# in the second equation and calculate #y#:
#y = -4x + 6# becomes:
#y = (-4 xx 1/2) + 6#
#y = -4/2 + 6#
#y = -2 + 6#
#y = 4#
The Solution Is:
#x = 1/2# and #y = 4#
Or
#(1/2, 4)#
