Recall that when we represent a system of equations with a matrix, we use the coefficients of the variables and the constant terms as the matrix elements. This is how it works.
Each row represents an equation
The first column represents the x variable's coefficients
The second column represents the y variable's coefficients
The last column represents the constant terms.
With this in mind, we can explicitly write the system of equations being represented by the matrix given in the exercise.
A=
[
cc|c
4 & 2 & 8
0 & 1 & 2
]
⇒ 4x+ 2y= 8 & (I) 1* y= 2 & (II)
Now we can think of a real-life situation we can model with this system. For example, x and y can represent the prices of different kind of candies — let's use bubble gum and chocolate bars, respectively.
Mathematical expressions and equations.
Verbal information
x
Price of a bubble gum
y
Price of a chocolate bar
y=2
The price of a chocolate bar is $2.
4x +2y=8
The total price for 4 bubble gums and 2 chocolate bars is $8.
Notice that this is only an example, as this system could represent infinitely many different situations.
