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)m+ a_(12)n=c_1 a_(21)m+ a_(22)n=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.
4m+ 1n=1 8m+ 4n=3
Now that we have identified all of the variables and constants, we can place them in a matrix.
[
cc|c
4 & 1 & 1
8 & 4 & 3
]
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 m= a and n= b. Let's solve the matrix!
We have found that m= 18 and n= 12. Now we can find x and y.
m=1/x=1/8 &⇒ x=8 [0.8em]
n=1/y=1/2 &⇒ y=2
The solution of the system is the point (8,2).
