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Applications of Linear Systems

Word problems using two equations and two unknowns

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The Bill of (Equal) Rights

Have you ever taken a close look at your cable TV, Internet, or phone bill? If you do, you’ll find that most service providers don’t charge a flat fee. For example, a cable provider might charge a connection fee when you first sign up for television service, followed by fees per month of use. An Internet provider might charge a monthly modem fee, and a cell phone provider might charge a flat monthly fee plus a per-minute rate for every minute over the number included in your mobile plan.

Why It Matters

If you and a friend were to compare bills, you might assume one of you pays less than the other based solely on the total amount due. But unless you dig deeper and take the added fees into consideration, you can’t accurately determine which one of you is actually getting a better deal. To draw such a conclusion, you’ll need to use a system of linear equations, and substitution is one method you can use to solve such equations.

Systems using substitution can help you calculate, for example, for how many minutes you and your friend can talk on your cell phone each month such that your bills equal the same amount. And if you find how many minutes result in your bills being equivalent, you’ll also know who is getting the better deal—it’s whoever can talk for more minutes!

See for yourself: http://www.youtube.com/watch?v=ac8lOVpATNY

Explore More

To learn more about the conditions that must be met in order to solve a system of equations by substitution, check out the following link.

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