# Solving Problems Using Linear Equations

Systems of linear equations can be used to model real-world problems.They can be solved using a number of different methods: These equations are already written in slope-intercept form, making them easy to graph.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.

Systems of linear equations can be used to model real-world problems.They can be solved using a number of different methods: These equations are already written in slope-intercept form, making them easy to graph.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.

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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.

In order to help Anne decide which to choose, we'll find where the two lines cross, by solving the two equations as a system.

Since equation 1 gives us an expression for y(0.25x 20), we can substitute this expression directly into equation 2: So if Anne uses 117.65 minutes a month (although she can't really do exactly that, because phone plans only count whole numbers of minutes), the phone plans will cost the same.

Since the number of minutes is the independent variable, it will be our x.

Cost is dependent on minutes - the cost per month is the dependent variable and will be assigned y.

Since we have 2 types of coins, let's call the number of nickels x and the number of dimes y.

We are given two key pieces of information to make our equations: the number of coins and their value.

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 per month, with calls costing an additional 25 cents per minute.