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 -2n=1 10m+ 20n=
Now that we have identified all of the variables and constants, we can place them in a matrix.
[
cc|c
4 & -2 & 1
10 & 20 &
]
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= 15 and n=- 110. Now we can find x and y.
m&=1/x= 1/5 ⇒ x=5
n&=1/y=-1/10 ⇒ y=-10
The solution of the system is the point (5,-10).
