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System of Linear Equations – Definition and Actual Life Examples



System of linear equations can come up naturally from many actual life examples. Typically talking, these issues come up when there are two unknowns or variables to unravel.

Within the determine above, there are two variables to unravel and they’re x and y. This type of system is known as system of linear equations with 2 variables.

Furthermore, a system of equations is a set of two or extra equations that have to be solved on the similar time. Because of this, a system may be referred to as simultaneous equations. The phrase simultaneous means “occurring on the similar time”

I’ll solely give you actual life examples that result in a system of linear equations and the way to arrange the system.

Actual-life conditions that result in a system of linear equations

Instance #1

The sum of two numbers is twenty and their distinction is ten. What are the 2 numbers?

Right here is the way to arrange the system:

Let x be the primary quantity

Let y be the second quantity

Then,

x + y = 20

x − y = 10

It’s also possible to write:

x + y = 20

y − x = -10

You’re going to get the identical solutions!

Instance #2

You’ve got 24 cash in your pockets which might be value 4.50 {dollars}. What number of cash are quarters? What number of cash are dimes?

Right here is the way to set it up:

Let q be the variety of quarters.

Let d be the variety of dimes.

Then,

q + d = 24

25 × q + 10 × d = 450

The second equation is hard. How did we get it?

Since 1 quarter equal to 25 cents, q quarter equal to 25 × q.

When you had 6 quarters and also you needed to know what number of cents are there for the 6 quarters, would you not do 6 × 25?

Simply say to your self that now as an alternative of 6 quarters you’ve q quarters. Does that make sense?

In the same means, since 1 dime equal to 10 cents, d dimes equal 10 × d.

What in regards to the 450? 4.50 {dollars} occasions 100 = 450 cents.

Lastly, since 25 × q represents what number of cents you’ve for quarters and 10 × d represents what number of cents you’ve for dimes, including them ought to equal to the whole of 450 cents.


Instance #3

A cellular phone plan gives 300 free minutes for a flat price of 20 {dollars}. In case your utilization exceed 300 minutes, you pay 50 cents for every minute.

A second cellular phone plan gives 500 free minutes for a flat price of 30 {dollars}. In case your utilization exceed 400 minutes, you pay 25 cents for every minute.

Mannequin the price of each plan with a system.

Right here is the way to arrange the system:

Let x be the variety of minutes you discuss.

Let y be the fee.

y = 20 + 0.50 (x – 300)

y = 30 + 0.25 (x – 500)

y = 20 + 0.50x – 150

y = 30 + 0.25x – 125

Subtract 0.50x from each side of the primary equation and subtract 0.25x from each side of the second equation.

We get:

y − 0.50 x = 20 – 150

y − 0.30 x = 30 – 125

y − 0.50 x = -130

y − 0.30 x = -95

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