If The Equations 2x+y=8 And X-2y=4 Represent The Two Sides Of A Triangle What Does The Other Side Equal? What Is The Equation For The Third Side And How Do I Solve The Equations?

Judging by the graphs of these equations (see picture), perhaps the other side of the triangle is x=0. The equation for the third side can be anything that
 - doesn't go through the point (4,0), i.e. the point where these lines intersect, and
 - isn't parallel to one of the other lines.
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To solve these equations for the point at which they intersect, you can do this.
1. Rewrite the equation so y is on one side by itself.
 2x+y=8
 y = 8-2x  (subtract 2x from both sides of the equation)

 x-2y=4
 x=4+2y  (add 2y to both sides)
 x-4=2y  (subtract 4 from both sides)
 (x-4)/2 = y  (divide both sides by 2)

2. Now, equate the two expressions for y
 (x-4)/2 = y = 8-2x

3. Solve for x
 (x-4)/2 = 8-2x
 x-4 = 2(8-2x)  (multiply both sides by 2)
 x-4 = 16-4x  (distributive law applied to right side)
 x+4x-4 = 16  (add 4x to both sides)
 x+4x = 16+4  (add 4 to both sides)
 x(1+4) = 20  (apply distributive law to left side, i.e. simplify)
 5x = 20
 x = 20/5 = 4  (divide both sides by 5)

4. Solve for y
 Pick the easiest expression to work with, and substitute the value of x
 (x-4)/2 = y
 (4-4)/2 = y
 0/2 = y
 0 = y

5. Put together what you know.
 The point of intersection is (x=4, y=0), or (4, 0).

There are many other ways to solve these equations, some of which may take fewer steps. Whatever you do, you need to remember that the "equal sign" is a sacred thing. You must always maintain its integrity by doing to the left side exactly the same thing you do to the right side. Remember that, and algebra will be a lot easier.

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