Step 1) Solve the first equation for #y#:
#4x - y = 14#
#4x - y + color(red)(y) - color(blue)(14) = 14 + color(red)(y) - color(blue)(14)#
#4x - 0 - color(blue)(14) = 14 - color(blue)(14) + y#
#4x - 14 = 0 + y#
#4x - 14 = y#
#y = 4x - 14#
Step 2) Substitute #4x - 14# for #y# in the second equation and solve for #x#:
#7x + 3y = 10# becomes:
#7x + 3(4x - 14) = 10#
#7x + (3 xx 4x) - (3 xx 14) = 10#
#7x + 12x - 42 = 10#
#19x - 42 = 10#
#19x - 42 + color(red)(42) = 10 + color(red)(42)#
#19x - 0 = 52#
#19x = 52#
#(19x)/color(red)(19) = 52/color(red)(19)#
#(color(red)(cancel(color(black)(19)))x)/cancel(color(red)(19)) = 52/19#
#x = 52/19#
Step 3) Substitute #52/49# for #x# in the solution to the first equation at the end of Step 1 and calculate #y#:
#y = 4x - 14# becomes:
#y = (4 xx 52/19) - 14#
#y = 208/19 - (19/19 xx 14)#
#y = 208/19 - 266/19#
#y = -58/49#
The solution is: #x = 52/19# and #y = -58/49 or #(52/19, -58/49)#
