[tex]\text{For}\ "<"\ \text{and}\ ">"\ \text{is dotted line}.\\\text{For}\ "\leq"\ \text{and}\ "\geq"\ \text{is solid line}.\\\text{For}\ "<"\ \text{and}\ "\leq"\ \text{shaded below a line}.\\\text{For}\ ">"\ \text{and}\ "\geq"\ \text{shaded above a line}.[/tex]
[tex]3x-9y<36\qquad\text{subtract 3x from both sides}\\\\-9y<-3x+36\qquad\text{change the signs}\\\\9y>3x-36\qquad\text{divide both sides by 9}\\\\y>\dfrac{3}{9}x-\dfrac{36}{9}\\\\y>\dfrac{1}{3}x-4\\\\y=\dfrac{1}{3}x-4\\\\for\ x=0\to y=\drac{1}{3}(0)-4=0-4=-4\to(0,\ -4)\\\\for\ x=3\to y=\dfrac{1}{3}(3)-=1-4=-3\to(3,\ -3)\\\\\text{dotted line and shaded above a line}[/tex]
[tex]24y-8x<48\qquad\text{add 8x to both sides}\\\\24y<8x+48\qquad\text{divide both sides by 24}\\\\y<\dfrac{8}{24}x+\dfrac{48}{24}\\\\y<\dfrac{1}{3}x+2\\\\for\ x=0\to y=\dfrac{1}{3}(0)+2=0+2=2\to(0,\ 2)\\\\for\ x=3\to y=\dfrac{1}{3}(3)+2=1+2=3\to(3,\ 3)\\\\\text{dotted line and shaded below a line}[/tex]
[tex](1,\ -2)\to x=1,\ y=-2\\\\\text{substitute}\\\\3x-9y<36\\\\3(1)-9(-2)<36\\\\3+18<36\\\\21<36\ CORRECT\\\\24y-8x<48\\\\24(-2)-8(1)<48\\\\-48-8<48\\\\-56<48\ CORRECT\\\\Answer:\ Yes.\ (1,\ -2)\ is\ a\ solution\ of\ system\ inequality.[/tex]
