# Solving Problems Using Linear Equations Since the number of minutes is the independent variable, it will be our x.

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We may be considering a purchase—for example, trying to decide whether it's cheaper to buy an item online where you pay shipping or at the store where you do not.

Or you may wish to join a CD music club, but aren't sure if you would really save any money by buying a new CD every month in that way. The first plan, with Vendafone, costs \$20 per month, with calls costing an additional 25 cents per minute.

If the equations were not written in slope-intercept form, you would need to simplify them first.

Once that is done, solving for Another way to solve a system of equations is by substitution.

In mathematics, a linear equation is one that contains two variables and can be plotted on a graph as a straight line.

A system of linear equations is a group of two or more linear equations that all contain the same set of variables.There are several ways to solve systems; we’ll talk about graphing first.Remember that when you graph a line, you see all the different coordinates (or \(x/y\) combinations) that make the equation work.Now, you can always do “guess and check” to see what would work, but you might as well use algebra!It’s much better to learn the algebra way, because even though this problem is fairly simple to solve, the algebra way will let you solve any algebra problem – even the really complicated ones.Now we need to look at the graph to see which plan is better if she uses more minutes than that, and which plan is better if she uses fewer.You can see that the Vendafone plan costs more when she uses more minutes, and the Sellnet plan costs more with fewer minutes.The first trick in problems like this is to figure out what we want to know.This will help us decide what variables (unknowns) to use.Or you might be considering two different phone contracts. The second company, Sellnet, charges per month, but calls cost only 8 cents per minute. You should see that Anne's choice will depend upon how many minutes of calls she expects to use each month.We start by writing two equations for the cost in dollars in terms of the minutes used.

## Comments Solving Problems Using Linear Equations

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Worked-out word problems on linear equations with solutions explained step-by-step in different types of examples. There are several problems which involve relations among known and unknown numbers and can be put in the form of equations.…

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