Maiclubk

2021-02-04

Solve the system of equations using Gaussian elimination
4x-8y=12
-x+2y=-3

Obiajulu

Step 1
The system of equations is given by,
4x-8y=12
-x+2y=-3
Step 2
Find the solution of system of equations, it is need to write an equivalent matrix equation AX=B .
$\left[\begin{array}{cc}4& -8\\ -1& 2\end{array}\right]\cdot \left[\begin{array}{c}x\\ y\end{array}\right]=\left[\begin{array}{c}12\\ -3\end{array}\right]$
Find the inverse matrix by using Gauss-Jordan elimination method.
That is, apply the row equivalent operations to the matrix.
Consider the matrix $A=\left[\begin{array}{cc}4& -8\\ -1& 2\end{array}\right]$.
Form of an augment matrix, in order to find the inverse matrix.
That is, form an matrix contains of A on the left side and the $2×2$ identify matrix on the right side.
$\left[\begin{array}{ccc}4& -8& 12\\ -1& 2& -3\end{array}\right]$
Step 3
Divide the first row by 4 as follows.
$\left[\begin{array}{ccc}1& -2& 3\\ -1& 2& -3\end{array}\right]$ New row $1=\frac{1}{4}$ row 1
Add the first and second rows as follows.
$\left[\begin{array}{ccc}1& -2& 3\\ 0& 0& 0\end{array}\right]$ New row 2 = row 1 + row 2
Thus, the system of equations has a solution set is $\left\{x-2y=3.$.
Step 4
The system of equations has a solution set $\left\{x-2y=3.$.