Answer
$a)False.\\b)True.$
Work Step by Step
$a)False,\:There\:is\:not\:only\:way\:to\:parametrically\:represent\:the\:solution\:set\:of\:a\:linear\:equation.\:For\:example.\\The\:linear\:equation\:x_1+2x_2=4.\\To\:find\:the\:solution\:set\:of\:an\:equation\:involving\:two\:variables,\:solve\:for\:one\:of\:the\:variables\:in\:terms\:of\:the\:other\:variable.\:Solving\:for\:x_1\:in\:terms\:of\:x_2,\:you\:obtain\:x_1=4-2x_2;\:By\:letting\:x_2=t,\:x_1=4-2t,\:x_2=t,\:t\:is\:any\:real\:number;\:x_1=s,\:x_2=2-\frac{1}{2}s,\:s\:is\:any\:real\:number.\\$
$\\b)True,\:for\:example\:the\:system\:of\:linear\:equations\:\begin{matrix}x+y=3\\ 2x+2y=6\end{matrix},\\This\:system\:has\:infinitely\:many\:solutions\:because\:the\:second\:equation\:is\:the\:result\:of\:multiplying\:both\:sides\:of\:the\:first\:equation\:by\:2.\:A\:parametric\:representation\:of\:the\:solution\:set\:is\:x=3-t,\:y=t,\:t\:is\:any\:real\:number.$
