Linear equations

Linear equations are all equations that have the following form: y = ax + b.

Linear equations

In y = ax + b, x is called independent variable and y is called dependent variable.

a and b are called constants.

y = 2x + 5 with a = 2 and b = 5,     y = -3x + 2 with a = -3 and b = 2,    and y = 4x + - 1 with a = 4 and b = -1 are other examples of linear equations.

Real life examples or word problems on linear equations are numerous.

More examples of linear equations

Consider the following two examples:

Example #1:

I am thinking of a number. If I add 2 to that number, I will get 5. What is the number?

Although it may be fairly easy to guess that the number is 3, you can model the situation above with a linear equation.

Let x be the number in my mind.

Add 2 to x to get 5.

Adding 2 to x to get 5 means that whatever x is, when I add 2 to x, it has to equal to 5.

The equation is 2 + x = 5

Example #2 :

Soon or later, all of us use the service of a taxi driver.

Taxi drivers usually charge an initial fixed fee as part of using their services. Then, for each mileage, they charge a certain amount.

Say for instance the initial fee is 4 dollars and each mileage cost 2 dollars.

The total cost can be modeled with an equation that is linear.

Let y be the total cost.

Let N be number of mileage.

Total cost = 4 + cost for N miles.

Notice that cost for N miles = N ×2.

Therefore, y = 4 + N × 2.

Say for instance, a taxi driver takes you to a distance of 20 miles, how much money do you have to pay using y = 4 + N × 2 ?

When N = 20, Y = 4 + 20 × 2 = 4 + 40 = 44 dollars

Now, let's ask the question the other way around!

If you pay 60 dollars, how far did the taxi driver took you?

This time y = 60

Replacing 60 into the equation gives you the following equation:

60 = 4 + N × 2

It is not obvious to see that N = 28.

That is why it is important to learn to solve linear equations!


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