Question

Hello!!! ) How are you? ) Can you help me please? More practice with systems of equations

Answer 1

`\text{For}\`

`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>(3)/(9)x-(36)/(9)\\\\y>(1)/(3)x-4\\\\y=(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=(1)/(3)(3)-=1-4=-3\to(3,\ -3)\\\\\text{dotted line and shaded above a line}`

`24y-8x<48\qquad\text{add 8x to both sides}\\\\24y<8x+48\qquad\text{divide both sides by 24}\\\\y<(8)/(24)x+(48)/(24)\\\\y<(1)/(3)x+2\\\\for\ x=0\to y=(1)/(3)(0)+2=0+2=2\to(0,\ 2)\\\\for\ x=3\to y=(1)/(3)(3)+2=1+2=3\to(3,\ 3)\\\\\text{dotted line and shaded below a line}`

`(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.`