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)#
