Question

Hello I'm stuck on this question and need help thank you

Answer 1

Step-by-step explanation

`\begin{gathered} -2x+3y\ge9 \\ x\ge-5 \\ y<6 \end{gathered}`

Step 1

graph the inequality (1)

a) isolate y

`\begin{gathered} -2x+3y\geqslant9 \\ add\text{ 2x in both sides} \\ -2x+3y+2x\geqslant9+2x \\ 3y\ge9+2x \\ divide\text{ both sides by 3} \\ (3y)/(3)\geqslant(9)/(3)+(2x)/(3) \\ y\ge(2)/(3)x+3 \end{gathered}`

b) now, change the symbol to make an equality and find 2 points from the line

`\begin{gathered} y=(2)/(3)x+3 \\ i)\text{ for x=0} \\ y=(2)/(3)(0)+3 \\ \text{sp P1\lparen0,3\rparen} \\ \text{ii\rparen for x=3} \\ y=(2)/(3)(3)+3=5 \\ so\text{ P2\lparen3,5\rparen} \end{gathered}`

now, draw a solid line that passes troguth those point

(0,3) and (3,5)

`y\geqslant(2)/(3)x+3\Rightarrow y=(2)/(3)x+3\text{\lparen solid line\rparen}`

as we need the values greater or equatl thatn the function, we need to shade the area over the line

Step 2

graph the inequality (2)

`x\ge-5`

this inequality represents the numbers greater or equal than -5 ( for x), so to graph the inequality:

a) draw an vertical line at x=-5, and due to we are looking for the values greater or equal than -5 we need to use a solid line and shade the area to the rigth of the line

Step 3

finally, the inequality 3

`y<6`

this inequality represents all the y values smaller than 6, so we need to draw a horizontal line at y=6 and shade the area below the line

Step 4

finally, the solution is the intersection of the areas

I hope this helps you