## Algebra - systems word problem

Quadratic equations and inequalities, variation equations, function notation, systems of equations, etc.
Divine
Posts: 5
Joined: Tue Oct 11, 2011 2:28 pm
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### Algebra - systems word problem

The math question in my book that I'm inquiring about has a picture, so I took a picture and uploaded the question. It's #65.

I've only got two linear equations in 3 variables. I needed one more to create a system of 3 equations in 3 variables.

This is what I did to get the two equations,

L = length of the wood
w = width of the wood
h = height of the table

-L + 32 + w = h
-w + 28 + L = h

The only other fact that I could determine besides those equations was this:

(-L +32 + w) + (-w + 28 +L) = 2h

This just states that if you add the two equations together, they equal twice the height. However, this solves to h = 30 cm because w and L cancel each other out, making it impossible to be used in my system.

30cm is the height, but what's weird is that I determined this without even making a system. I need to know how to get the system though, so that I can figure out L and w.

I'm really determined to figure this out, so help would be appreciated.

maggiemagnet
Posts: 358
Joined: Mon Dec 08, 2008 12:32 am
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### Re: Algebra - systems word problem

L = length of the wood
w = width of the wood
h = height of the table

-L + 32 + w = h
-w + 28 + L = h
You can kind of cheat. Since you don't actually care what L and w are, you can do "L - w = x". Then you have these equations:

. . . . .32 - x = h
. . . . .28 + x = h

Then 60 = 2h, and so forth.