# Algebra

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define the following new variables

X to A =W
X to B =X
Y to A =Y
Y to B =Z

w+x=32
y+z=8
w+y=22
x+z=18

You helped me solve for y Ijust added w+y=32

220w+300(32-w)+400(22-w)+180(8-y)=9280

,

w+y=22

The answer I got was y=32 I solved for x and got x=42 I don't know if this is right. I am trying to solve for w and z but keep coming up with fractions. I am using the substitution method to calculate. Thank you Can you help me understand.

• Algebra - ,

It is not clear to me what this parts means:
"define the following new variables
X to A =W
X to B =X
Y to A =Y
Y to B =Z "

However, if we look at the system of 4x4 equations:
w+x=32
y+z=8
w+y=22
x+z=18

Whichever method you use, you will find that one of the equations is a linear combination of the other three, and there is an infinite number of solutions, depending on the value of the "free variable".

If we take the "free variable" as z, then we can express the solution in terms of z, as follows:
w=t+14, x=18-t, y=8-t, z=t