Question

HELP PLEASE!!!!!!!!!!! System Of Inequalities!!! please help me number 3 and 4 please

Answer 1

`\text{For}\`

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`3.\\y\leq(4)/(3)x-1\\\\y=(4)/(3)x-1\\\\for\ x=0\to y=(4)/(3)(0)-1=0-1=-1\to(0;\ -1)\\\\for\ x=3\to y=(4)/(3)(3)-1=4-1=3\to(3,\ 3)\\\\\text{solid line and shaded below a line}`

`2x+3y>15\qquad\text{subtract 2x from both sides}\\\\3y>-2x+15\qquad\text{divide both sides by 3}\\\\y>-(2)/(3)x+5\\\\y=-(2)/(3)x+5\\\\for\ x=0\to y=-(2)/(3)(0)+5=0+5=5\to(0;\ 5)\\\\for\ x=3\to y=-(2)/(3)(3)+5=-2+5=3\to(3;\ 3)\\\\\text{dotted line and shaded abowe a line}`

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`4.\\y<2x-8\\\\y=2x-8\\\\for\ x=0\to y=2(0)-8=0-8=-8\to(0;\ -8)\\\\for\ x=4\to y=2(4)-8=8-8=0\to(4;\ 0)\\\\\text{dotted line and shaded below a line}\\\\\\5x+3y\geq9\qquad\text{subtract 5x from both sides}\\\\3y\geq-5x+9\qquad\text{divide both sides by 3}\\\\y\geq-(5)/(3)x+3\\\\y=-(5)/(3)x+3\\\\for\ x=0\to y=-(5)/(3)(0)+3=0+3=3\to(0;\ 3)\\\\for\ x=3\to y=-(5)/(3)(3)+3=-5+3=-2\to(3;\ -2)\\\\\text{solid line and shaded above a line}`