No, but eliminating variables is one of several ways to find the value of variables in a system of equations.
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Assuming the simplest case of two equations in two variable: solve one of the equations for one of the variables. Substitute the value found for the variable in all places in which the variable appears in the second equation. Solve the resulting equation. This will give you the value of one of the variables. Finally, replace this value in one of the original equations, and solve, to find the other variable.
They are alike because the both have value, they both have variables, and both have numbers. there, happy?
Finding a set of value for the set of variables so that, when these values are substituted for the corresponding variables, all the equations in the system are true statements.
A single equation with two variables can be solved for one of the variables, in terms of the other. For example, a rectangle's area is A = wh (width x height). Now let's assume you know the area: 20 = wh. You can solve for any of these variables in terms of the other, for example, w = 20/h. That is, once you assign a value to "h", you can calculate "w". But you don't know the specific values for "w" and "h", because the equation has an infinite number of solutions.If you want to know specific values for the variables, in general, you need two different equations with 2 variables - or 3 equations with 3 variables, etc.