**Step 1)** Solve the second equation for #x#:

#x + 4y = 14#

#x + 4y - color(red)(4y) = 14 - color(red)(4y)#

#x + 0 = 14 - 4y#

#x = 14 - 4y#

**Step 2)** Substitute #(14 - 4y)# for #x# in the first equation and solve for #y#:

#2x - 4y = 4# becomes:

#2(14 - 4y) - 4y = 4#

#(2 * 14) - (2 * 4y) - 4y = 4#

#28 - 8y - 4y = 4#

#28 + (-8 - 4)y = 4#

#28 + (-12)y = 4#

#28 - 12y = 4#

#-color(red)(28) + 28 - 12y = -color(red)(28) + 4#

#0 - 12y = -24#

#-12y = -24#

#(-12y)/color(red)(-12) = (-24)/color(red)(-12)#

#(color(red)(cancel(color(black)(-12)))y)/cancel(color(red)(-12)) = 2#

#y = 2#

**Step 3)** Substitute #2# for #y# in the solution to the second equation at the end of **Step 1** and calculate #x#:

#x = 14 - 4y# becomes:

#x = 14 - (4 * 2)#

#x = 14 - 8#

#x = 6#

**The Solution is:** #x = 6# and #y = 2# or #(6, 2)#