Solving Problems Using Linear Equations

Solving Problems Using Linear Equations-25
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.

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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.

Students need to use a pronumeral to represent the unknown number They then need to write an equation and solve it to find the value of the unknown number.

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Systems of equations crop up frequently in problems that deal with mixtures of two things—chemicals in a solution, nuts and raisins, or even the change in your pocket! Janine empties her purse and finds that it contains only nickels (worth 5 cents each) and dimes (worth 10 cents each).

If she has a total of 7 coins and they have a combined value of 45 cents, how many of each coin does she have?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.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.What we want to know is how many pairs of jeans we want to buy (let’s say “\(j\)”) and how many dresses we want to buy (let’s say “\(d\)”).Always write down what your variables will be: equations as shown below.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.


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