Question

Which ordered pair would be a solution on the graph of the following system of inequalities: y is greater than or equal to negative one-half times x minus 8 and y is less than 8 times x plus 2?

Answer 1

Ordered pair is
`( x, y)= ( (20)/(17) , (-126)/(17) )`

Explanation:

We have the following inequalities:

`y \geq (-x)/(2) - 8` and
`y < 8x +2` . In order to find ordered pair would be a solution on the graph .Let's solve both inequalities , and will take common solution from both of them !

`y = (-x)/(2) - 8 \\` and ,
`y = 8x +2` which implies:

⇒
`8x + 2 = (-x)/(2) - 8`

⇒
`(17x)/(2) = - 10`

⇒
`x = (-20)/(17)`

putting value of x in both inequalities we get,

`y \geq (-x)/(2) - 8` and
`y < 8x +2`

`y \geq (-((-20)/(17) ))/(2) - 8` and
`y < 8.((-20)/(17)) + 2`

`y \geq (-126)/(17)` and
`y < (-126)/(17)`

Hence at x =
`(-20)/(17)` and y =
`(-126)/(17)` above inequalities are satisfied. ∴ Ordered pair is
`( x, y)= ( (20)/(17) , (-126)/(17) )`