Create A System Of Linear Equations From Your Own Life, It Can Be An Extension Of Your Module 2 SLP Or Something New Entirely. Keep In Mind That A System Of Linear Equations Will Consist Of Two Equations Using The Same Variables And The Variables?

A linear system taken from an individual's life could be expressed as follows:
There are 22 people taking part in a coach tour. When they stop for lunch, some have hamburgers, while the others opt for hotdogs. The waiter brings eight more hotdogs than hamburgers to the table.

How many were purchased of each?

X = number of hotdogs
y = number of hamburgers

The equations are therefore:
X + y = 22
x = y + 8

To determine y, we proceed as follows:
Y + 8 + y = 22
2y + 8 = 22
2y = 22 - 8
y = (22-8) / 2
y = 7

It is now easily possible to determine x:
X = y + 8
x = 7 + 8
x = 15

The group of travelers purchased seven hamburgers and 15 hotdogs.

• Brief explanation of Linear Systems

Linear algebra is fundamental in modern mathematics. So-called computational algorithms to find solutions are important within numerical linear algebra, in particular in fields such chemistry, physics, economics, computer science and engineering. Linear systems, which are a part of linear algebra, assist in approximating non-linear equations. This is helpful especially in the process of creating computer simulations of fairly complex systems or mathematical models.

• Basic Example

The simplest form of a linear system consists of two variables, x and y, within two equations, for instance:

X + y = 21 and
x = y + 7

These equations can be combined into one by substituting the x in the first one with y + 7. The new equation therefore looks like this: Y + 7 + y = 21. This can be shortened into: 2y + 7 = 21, then 2y = 21 - 7. Consequently, y = 14/2 = 7. We know that x = y + 7, so x = 14.

• Consistent or Inconsistent?

A linear system can be regarded as consistent, as it can be used to linearize any set of two or more non-linear equations.