Exercise 3

Use Gauss’s Method to solve each system or conclude ‘many solutions’ or ‘no solutions’.

• (a)  $\begin{array}{rcrcr}2x&+&2y&=&5\\ x&-&4y&=&0\end{array}$     (b)  $\begin{array}{rcrcr}-x&+&y&=&1\\ x&+&y&=&2\end{array}$     (c)  $\begin{array}{rcrcrcr}x&-&3y&+&z&=&1\\ x&+&y&+&2z&=&14\end{array}$     (d)  $\begin{array}{rcrcr}-x&-&y&=&1\\ -3x&-&3y&=&2\end{array}$     (e)  $\begin{array}{rcrcrcr}&&4y&+&z&=&20\\ 2x&-&2y&+&z&=&0\\ x&&&+&z&=&5\\ x&+&y&-&z&=&10\end{array}$     (f)  $\begin{array}{rcrcrcrcr}2x&&&+&z&+&w&=&5\\ &&y&&&-&w&=&-1\\ 3x&&&-&z&-&w&=&0\\ 4x&+&y&+&2z&+&w&=&9\end{array}$