Linear Equation

Word or story problems give us a first glimpse into how mathematics is used in the real word. To be solved, a word problem must be translated into the language of mathematics, where we use symbols for numbers - known or unknown, and for mathematical operations. When all is said and done, a word problem, stripped from inessential details, translates into one or more mathematical equations of one kind or another. After the equations have been solved, the result can be translated back into the ordinary language.

When translating a word problem into the mathematical language seek the essential. Inessential can be modified without affecting the meaning of the problem.

A variable in an equation is just an unknown quantity. Its name is quite arbitrary.

Think of a problem class to which the given problem belongs.

An equation may be less restrictive than the original problem. Check the answer against the problem's background.

Translate the wording into a numeric equation

that combines smaller "expressions"

Read the problem, sketch the proper picture, and label variables.

Write down what the answer should look like.

Come up with the appropriate formula.

Solve for the needed variable.

Plug in the known numbers

Sometimes the problem lies in understanding the problem. If you are unclear as to what needs to be solved, then you are probably going to get the wrong results. In order to show an understanding of the problem you of course need to read the problem carefully. Sounds simple enough, but some people jump the gun and try to start solving the problem before they have read the whole problem. Once the problem is read, you need to list out all the components and data that are involved. This is where you will be assigning your variables.

In the problems on this page, we will be letting each unknown be a separate variable. So, if you have two unknowns, you will have two variables, x and y. If you have three unknowns, you will have three variables, x, y, and z. . When you devise a plan (translate), you come up with a way to solve the problem. Setting up an equation, drawing a diagram, and making a chart are all ways that you can go about solving your problem. In the problems on this page, we will be setting up systems of linear equations. The number of equations needs to match the number of unknowns. For example, if you have two variables, then you will need two equations. If you have three variables, then you will need three equations The next step, carry out the plan (solve), is big. This is where you solve the system of equations you came up with in your devise a plan step. The equations in the systems in this tutorial will all be linear equations In problem solving it is good to look back (check and interpret).. Basically, check to see if you used all your information and that the answer makes sense. If your answer does check out make sure that you write your final answer with the correct labeling.