Question

Solve the system by using elementary row operations on the equations. Follow the systematic elimination procedure. x 1 plus 2 x 2x1+2x2 equals= negative 4−4 3 x 1 plus 8 x 23x1+8x2 equals= negative 8−8 Find the solution to the system of equations.

Answer 1

Answer:

The solution to the system is:

$\begin{array}{ccc}x_1&=&-8\\x_2&=&2\end{array}$

Step-by-step explanation:

To find the solution to the system of linear equations

$\left\begin{array}{cccccc}x_1&+&2x_2&=&-4\\3x_1&+&8x_2&=&-8\end{array}\right$

using elementary row operations.

First, state the problem in matrix form. A matrix is a grid of numbers without the vertical line.

$\left[\begin{array}{cc|c}1&2&-4\\3&8&-8\end{array}\right]$

This is called an augmented matrix. The word “augmented” refers to the vertical line, which we draw to remind ourselves where the equals sign belongs.

Now,

Row Operation 1: add -3 times the 1st row to the 2nd row

$\left[\begin{array}{cc|c}1&2&-4\\0&2&4\end{array}\right]$

Row Operation 2: multiply the 2nd row by 1/2

$\left[\begin{array}{cc|c}1&2&-4\\0&1&2\end{array}\right]$

Row Operation 3: add -2 times the 2nd row to the 1st row

$\left[\begin{array}{cc|c}1&0&-8\\0&1&2\end{array}\right]$

Next, interpret the reduced row echelon form

$\left[\begin{array}{cc|c}1&0&-8\\0&1&2\end{array}\right] \rightarrow \begin{array}{ccc}x_1&=&-8\\x_2&=&2\end{array}$

The solution to the system is:

$\begin{array}{ccc}x_1&=&-8\\x_2&=&2\end{array}$