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 $( x, y)= ( \frac{20}{17} , \frac{-126}{17} )$

Step-by-step explanation:

We have the following inequalities:

$y \geq \frac{-x}{2} - 8$ 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 !

$y = \frac{-x}{2} - 8$ and , $y = 8x +2$ which implies:

⇒$8x + 2 = \frac{-x}{2} - 8$

⇒$\frac{17x}{2} = - 10$

⇒ $x = \frac{-20}{17}$

putting value of x in both inequalities we get,

$y \geq \frac{-x}{2} - 8$ and $y < 8x +2$

$y \geq \frac{-(\frac{-20}{17} )}{2} - 8$ and $y < 8.(\frac{-20}{17}) + 2$

$y \geq \frac{-126}{17}$ and $y < \frac{-126}{17}$

Hence at x = $\frac{-20}{17}$ and y  = $\frac{-126}{17}$ above inequalities are satisfied. ∴ Ordered pair is $( x, y)= ( \frac{20}{17} , \frac{-126}{17} )$