In the matrix form of the system, the coefficients of the variables form the columns on the left-hand side of the bar and the constants form the column on the right-hand side of the bar.
System of Equations: 5x+2y=0.23 7x+5y=0.41 Matrix Form:
[
cc|c
5 & 2 & 0.23
7 & 5 & 0.41
]
Practice makes perfect
We are given the prices of the packages that consist of erasers and pencils. We will write a system of equations that represents the situation. Then we will write a matrix to represent the system.
System of Equations
To write a system that represents the situation, we should first define the unknowns. In this situation, the unknowns are the prices of a eraser and a pencil.
Price of a Eraser:& x
Price of a Pencil:& y
Now we can make an organized table to write the equation that form a system.
Package I
Package II
Verbal Expression
Algebraic Expression
Verbal Expression
Algebraic Expression
Number of erasers
5
Number of erasers
7
Price of the erasers
5 x
Price of the erasers
7 x
Number of pencils
2
Number of pencils
5
Price of the pencils
2 y
Price of the pencils
5 y
Price of the package is $.23
5 x+ 2 y=0.23
Price of the package is $.41
7 x+ 5 y=0.41
Therefore, we have two equations that we can use to form a system.
5x+2y=0.23 7x+5y=0.41
Matrix Form
To rewrite the system of equations as a matrix, we need to consider how the elements of the system relate to the elements of a matrix.
The equals signs in the system of equations are represented with a vertical bar in the matrix.
The coefficients of the variables form the columns on the left-hand side of the bar.
The constants form the column on the right-hand side of the bar.
Below we demonstrate this in a generalized form.
a_(11)x+ a_(12)y=c_1 a_(21)x+ a_(22)y=c_2
⇕
[
cc|c
a_(11) & a_(12) & c_1
a_(21) & a_(22) & c_2
]
When each equation in the system is written in the same order, we can consider the coefficients of the variables and the constants.
5x+ 2y=0.23 7x+ 5y=0.41
Now that we have identified all of the variables and constants, we can place them in a matrix.
[
cc|c
5 & 2 & 0.23
7 & 5 & 0.41
]
