To solve for the variables w, x, y, and z in the given system of equations, we can use the substitution method. Let's go through the steps together:
1. We are given the equations:
w + x = 32 (Equation 1)
y + z = 8 (Equation 2)
w + y = 22 (Equation 3)
x + z = 18 (Equation 4)
2. You mentioned that you solved for y and got y = 32 by adding w + y = 32. However, this equation contradicts equation 3 (w + y = 22). Since these two equations cannot be true simultaneously, there seems to be an error in one of them. Let's stick to equation 3 for now: w + y = 22.
3. To solve for w, we can use equation 3 and subtract y from both sides:
w = 22 - y (Equation 5)
4. Now, let's substitute equation 5 into equation 1 to solve for x:
(22 - y) + x = 32
x = 32 - 22 + y
x = 10 + y (Equation 6)
5. Next, we can substitute equations 5 and 6 into equation 2 to solve for z:
y + z = 8
y + z = 8
y + (8 - y) = 8
y - y + z = 8 - 8
z = 0 (Equation 7)
6. Finally, we have found the values of w, x, y, and z:
w = 22 - y
x = 10 + y
y = y
z = 0
Please note that the equation you mentioned, "w + y = 32," is not consistent with the given system of equations, and it seems that there may have been a mistake in solving for y.
If you have any more specific questions or need further assistance, feel free to ask!