Question

Derive the systems of inequalities for the graph below please

Answer 1

y ≥ x + 9 and 15x + 4y + 40 > 0

Explanation:

The firm line passes through the x-intercept (-9,0) and the y-intercept (0,9) so, the equation of the firm line is

`(x)/(- 9) + (y)/(9) = 1`

⇒ -x + y = 9

⇒ y = x + 9

Now, the origin is not in the solution zone of the firm line inequality.

So, the inequality will be y ≥ x + 9 ........ (1)

Again, the dotted line passes through the points (-4,5) and (0,-10)

Therefore, the equation of the dotted line will be

`(y + 10)/(- 10 - 5) = (x - 0)/(0 + 4)`

⇒ 4y + 40 = - 15x

⇒ 15x + 4y + 40 = 0

Now, the dotted line inequality includes origin (0,0) in the solution zone.

So, the dotted line inequality will be 15x + 4y + 40 > 0 ......... (2)

Therefore, the system of inequalities for the graph will be from (1) and (2),

y ≥ x + 9 and 15x + 4y + 40 > 0 (Answer)