Step 1) Solve the second equation for #x#:
#x + 6y = 4#
#x + 6y - color(red)(6y) = 4 - color(red)(6y)#
#x + 0 = 4 - 6y#
#x = 4 - 6y#
Step 2) Substitute #(4 - 6y)# for #x# in the first equation and solve for #y#:
#2x + 3y = 2# becomes:
#2(4 - 6y) + 3y = 2#
#(2 xx 4) - (2 xx 6y) + 3y = 2#
#8 - 12y + 3y = 2#
#8 + (-12 + 3)y = 2#
#8 + (-9)y = 2#
#8 - 9y = 2#
#8 - color(red)(8) - 9y = 2 - color(red)(8)#
#0 - 9y = -6#
#-9y = -6#
#(-9y)/color(red)(-9) = (-6)/color(red)(-9)#
#y = 2/3#
Step 3) Substitute #2/3# for #y# in the solution to the second equation at the end of Step 1 and calculate #x#:
#x = 4 - 6y# becomes:
#x = 4 - (6 xx 2/3)#
#x = 4 - 12/3#
#x = 4 - 4#
#x = 0#
The Solution Is:
#x = 0# and #y = 2/3#
Or
#(0, 2/3)#
