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.

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.

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

- Basic Example

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?