Question

Graph the solution to the following system of inequalities. Choose one point in the solution of the system and prove it

mathematically.
2x - 3y<=6
y< -1/2x
Include the graph of the system of inequalities and the proof of the solution.

Answer 1

Explanation:

`2x - 3y\leq 6` ==>
`y\leq (2)/(3)x-2`

`y < -(1)/(2) x`

`2x - 3y\leq 6`

`-2x`
`-2x`

`-3y\leq -2x+6`

`(-3y)/(-3) \leq (-2x+6)/(-3)`

`y\geq (2)/(3)x-2`

`y\geq (2)/(3)x-2`

`y < -(1)/(2) x`

Check you answer using (-1,-1)

`y\geq (2)/(3)x-2`

`-1\geq (2)/(3)(-1)-2`

`-1\geq -(2)/(3)-2`

`-1\geq -(2)/(3)-(6)/(3)`

`-1\geq -(8)/(3)`

`-3(-1\geq -(8)/(3))`

`3\geq 8`

True statement

Hope this helps!