Question

Write each system of linear equations as an augmented matrix:

Part (a): $\left\{\begin{array}{l}3x-y=-1\\ 2y=2x+5\end{array}\right.$

Part (b): $\left\{\begin{array}{l}4x+3y=-2\\ x-2y-3z=7\\ 2x-y+2z=-6\end{array}\right.$

Short answer

Part (a): The augmented matrix is $\left[\begin{array}{rrr}3& -1& -1\\ -2& 2& 5\end{array}\right]$.

Part (b): The augmented matrix is $\left[\begin{array}{cccr}4& 3& 0& -2\\ 1& -2& -3& 7\\ 2& -1& 2& -6\end{array}\right]$.

Step-by-step solution

Part (a) Step 1. Given information.

Consider the given system of equations,

$\left\{\begin{array}{l}3x-y=-1\\ 2y=2x+5\end{array}\right.$

Here, the second equation is not in standard form.

Rewrite the second equation in standard form,

localid="1645427129270" $\begin{array}{rcl}2y& =& 2x+5\\ -2x+2y& =& 5\end{array}$

Part (a) Step 2. Write in augmented matrix.

Write the standard form of the second equation,

$\left\{\begin{array}{l}3x-y=-1\\ -2x+2y=5\end{array}\right.$

Write the augmented matrix,

$\left[\begin{array}{rrr}3& -1& -1\\ -2& 2& 5\end{array}\right]$

Part (b) Step 1. Given information.

Consider the given system of equations,

$\left\{\begin{array}{l}4x+3y=-2\\ x-2y-3z=7\\ 2x-y+2z=-6\end{array}\right.$

Here all the equations are in the standard form.

Write the augmented matrix,

$\left[\begin{array}{cccr}4& 3& 0& -2\\ 1& -2& -3& 7\\ 2& -1& 2& -6\end{array}\right]$