Question

The following inequalities form a system. y is greater than or equal to two-thirds times x plus 1 y is less than negative one-fourth times x plus 2 Which ordered pair is included in the solution to this system? (−6, 3.5) (−6, −3) (−4, 3) (−4, 4)

Answer 1

Answer: (−6, −3)

Explanation:

First, we will write out the given inequalities.

y is greater than or equal to two-thirds times x plus 1

y ≥
`(2)/(3)`x + 1

y is less than negative one-fourth times x plus 2

y <
`(1)/(4)`x + 2

Now that we have our two given inequalities, we can solve. To do this, we will graph (see attached) both of the inequalities and all of the given points. The point must be within the solution set for both inequalities to be a valid solution.

The only valid ordered pair is (−6, −3).