# Gaussian Method

## 1.17 Solving 

### a.
$$
\begin{flalign}

2x + 3y &= 13 &\\\
x - y &= -1\\

&\rightarrow (2p2 - p1) &\\\

   5y &= 15 \\
x - y &= -1 \\

&\rightarrow (\text{swap } p1 / p2) &\\\

x - y &= -1 \\
   5y &= 15 \\
\\
y &= 3 \\
x &= 2 \\

\end{flalign}
$$

### b.

$$
\begin{flalign}
 x -     z &= 0 &\\\
3x + y     &= 1 \\
-x + y + z &= 4\\
\\
\rightarrow& p3 + p1 \\
 x -     z &= 0 \\
3x + y     &= 1 \\
         y &= 4\\
\\
x = -1\\
y = 4\\
z = -1
\end{flalign}
$$

## Finding type of solutions

## 1.18
### a.

$$
\begin{flalign}
−3x + 2y &= 0 &\\\
−2y &= 0 \\
&\rightarrow \text{One solution}
\end{flalign}
$$
### b.

$$
\begin{flalign}
x + y &= 4 &\\
y − z &= 0 \\
&\rightarrow \text{Infinitely many, now row leading with z}
\end{flalign}
$$


$$
\begin{flalign}
−3x + 2y &= 0 &\\\
−2y &= 0 \\
&\rightarrow \text{One solution}
\end{flalign}
$$
## 1.19

## a.
$$
\begin{flalign}
2x +  2y  &=  5  &\\\
x  -  4y  &=  0 \\

\rightarrow & -\frac{1}{2}p1 + p2 \\

2x +  2y  &=  5  &\\\
   - 5y &= -2.5 \\
\\
y &= \frac{1}{2}\\
x &= 2

\end{flalign}
$$