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When solving linear equations, the first and most crucial step is to 'isolate the variable'. This means to rearrange the equation so that the variable we are solving for is by itself on one side of the equality sign. Isolating the variable makes the solution straightforward to find. For instance, in the exercise given, we begin by isolating the variable term 'y'.

This is done by ensuring that all terms containing the variable are on one side and all other terms are on the opposite side. We achieve this by performing the same operation on both sides of the equation, which maintains the balance. In our example, we subtracted 4y from each side to start isolating 'y'. This simplified the equation to just one instance of 'y', hence making the next steps easier and clearer.

Solving a linear equation step by step is akin to following a recipe: each action builds upon the previous step leading to the final solution. After isolating the variable, subsequent steps typically involve simplifying the equation further to find the value of the variable.

In our equation, the next step after isolation was to remove any constants attached to the variable. We subtracted 1.8 from both sides, which allowed us to obtain 'y' on its own. It is these logical and sequenced steps that make up the essence of solving linear equations methodically. By approaching equations in this manner, students can solve even more complex problems with consistent methods and clear understanding.

After finding a potential solution to an equation, it is vital to make sure that this solution is actually correct. Checking the solution involves substituting the variable back into the original equation and verifying that both sides are equal.

For the exercise at hand, substituting y = -5 back into the original equation should result in an identity, confirming the solution. If after the substitution both sides of the equation balance out, as in our example where we ended up with -23.2 = -23.2, it reassures us that our solution is indeed correct. This critical step not only verifies our answer but also enhances our understanding of the relationship between the components of the equation.