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.
2x+ 3y=13 5x+ 7y=31
Now that we have identified all of the variables and constants, we can place them in a matrix.
[
cc|c
2 & 3 & 13
5 & 7 & 31
]
Solving the Matrix
In order to solve the matrix, we will use row operations to obtain a matrix in the following form.
[
cc|c
1 & 0 & a
0 & 1 & b
]
This final matrix represents the solution of the system of equations, where x= a and y= b. Let's solve the matrix!
