Step 1)Solve both equations for #-9w#:
#-3w + z = 4#
#color(red)(3)(-3w + z) = color(red)(3) xx 4#
#(color(red)(3) xx -3w) + (color(red)(3) xx z) = 12#
#-9w + 3z = 12#
#-9w + 3z - color(red)(3z) = 12 - color(red)(3z)#
#-9w + 0 = 12 - 3z#
#-9w = 12 - 3z#
#-9w + 5z = -1#
#-9w + 5z - color(red)(5z) = -1 - color(red)(5z)#
#-9w + 0 = -1 - 5z#
#-9w = -1 - 5z#
Step 2)* Now that the left side of each equation is equal we can equate the right side of each equation and solve for #z#
#12 - 3z = -1 - 5z#
#12 - color(red)(12) - 3z + color(blue)(5z) = -1 - color(red)(12) - 5z + color(blue)(5z)#
#0 + (-3 + color(blue)(5))z = -13 - 0#
#2z = -13#
#(2z)/color(red)(2) = -13/color(red)(2)#
#(color(red)(cancel(color(black)(2)))z)/cancel(color(red)(2)) = -13/2#
#z = -13/2#
Step 3) Substitute #-13/2# for #z# in the solution to either equation in Step 1 and solve for #w#:
#-9w = 12 - 3z# becomes:
#-9w = 12 - (3 xx -13/2)#
#-9w = 12 - (-39/2)#
#-9w = 12 + 39/2#
#-9w = (2/2 xx 12) + 39/2#
#-9w = 24/2 + 39/2#
#-9w = (24 + 39)/2#
#-9w = 63/2#
#1/color(red)(-9) xx -9w = 1/color(red)(-9) xx 63/2#
#1/cancel(color(red)(-9)) xx color(red)(cancel(color(black)(-9)))w = -63/18#
#w = -7/2#
The Solution Is:
#w = -7/2# and #z = -13/2#