The three primary ways are:
- writing an equation
- drawing a diagram
- reading a table
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It might depend on the exact circumstances. Often, you would solve an equation to achieve that.
They can be, but not always. Other methods (equations, graphs) may be the best way.
In real life its not useful, unless you're going to need geometry in the career you choose.
That depends on the equation. In general, you'll try to isolate the variable, by using operations (on both sides of the equation) that get rid of anything other than the variable, on the side the variable is on.
No, but eliminating variables is one of several ways to find the value of variables in a system of equations.