Use the Gauss-Jordan method to solve the following system of equations.
$\begin{matrix} x + y = 8 \\ 3 x + 2 y = 18 \end{matrix}$

Answer

Expert–verified

Hide Steps

Answer

Final Answer: The solution to the system of equations is $x = 2$ and $y = 6$ .

Steps

Step 1 ：Represent the system of equations as an augmented matrix: $\begin{array}{ccc} 1 & 1 & 8 \\ 3 & 2 & 18 \end{array}$

Step 2 ：Transform the matrix into a form where the leading coefficient of each row is 1, and all other numbers in the column containing the pivot are 0. The transformed matrix is: $\begin{array}{ccc} 1 & 1 & 8 \\ 0 & 1 & 6 \end{array}$

Step 3 ：The first row of the matrix corresponds to the equation $x + y = 8$ , and the second row corresponds to the equation $y = 6$ . Therefore, the solution to the system of equations is $x = 8 - y = 2$ and $y = 6$ .

Step 4 ：Final Answer: The solution to the system of equations is $x = 2$ and $y = 6$ .

Use the Gauss-Jordan method to solve the following system of equations.x+y=83x+2y=18

Answer

Popular Problems

Use the Gauss-Jordan method to solve the following system of equations.
$\begin{matrix} x + y = 8 \\ 3 x + 2 y = 18 \end{matrix}$