Chapter 1.1, Problem 3E

In each of the following systems, interpret each equation as a line in the plane. For each system, graph the lines and determine geometrically the number of solutions.

(a) $\begin{array}{l}{x}_1+x_2=4\\ x_1-x_2=2\end{array}$

(b) $\begin{array}{l}{x}_1+2x_2=4\\ -x_1-4x_2=4\end{array}$

(c) $\begin{array}{l}2x_1-x_2=3\\ -4x_1+2x_2=-6\end{array}$

(d) $\begin{array}{l}{x}_1+x_2=1\\ x_1-x_2=1\\ -x_1+3x_2=3\end{array}$