Chapter 8.1, Problem 55E

To determine

To solve: The system of linear equations given augmented matrix form using back-substitution.

Answer to Problem 55E

The solution of the system is $x=2$ and $y=-1$ .

Explanation of Solution

Given information:

The augmented matrix is

  $\left[\begin{array}{cccc}1& -2& :& 4\\ 0& 1& :& -1\end{array}\right]$

Calculations:

Since the number of rows in given augmented matrix is 2, lets consider $x$ and $y$ as variables.

Thus, writing it in the equations form, we have

  $\{\begin{array}{c}x-2y=4\\ y=-1\end{array}$

Substituting $y=-1$ in the first equation,

  $\begin{array}{l}x-2(-1)=4\\ \Rightarrow x+2=4\\ \Rightarrow x=2\end{array}$

Conclusion:

Therefore, the solution of the system is $x=2$ and $y=-1$ .