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