Question

Which ordered pairs are solutions to the inequality 4x+y>−6?

(2, 0)

(−3, 6)

(4, −20)

(0, −9)

(−1, −1)

Answer 1

After testing each ordered pair by substituting into the inequality
`4x+y > -6`, the pairs
`(2, 0) and (-1, -1)` satisfy the inequality, hence they are the solutions.

Step-by-step explanation:

To determine which ordered pairs are solutions to the inequality
`4x+y > −6` we need to substitute the
`x and y` values from each pair into the inequality and check if the inequality holds true.

• For
  `(2, 0)`, we get
  `4(2) + 0 > -6`, which simplifies to
  `8 > -6`. This is true, so
  `(2, 0)`is a solution.
• For
  `(−3, 6)`, we get
  `4(−3) + 6 > -6`, which simplifies to
  `-12 + 6 > -6.`This is false, so
  `(−3, 6)` is not a solution.
• For
  `(4, −20)`, we get
  `4(4) + (−20) > -6`, which simplifies to
  `16 - 20 > -6`. This is false, so
  `(4, −20)` is not a solution.
• For
  `(0, −9)`, we get
  `4(0) + (−9) > -6`, which simplifies to
  `-9 > -6`. This is false, so
  `(0, −9)` is not a solution.
• For
  `(−1, −1)`, we get
  `4(−1) + (−1) > -6`, which simplifies to
  `-4 - 1 > -6`. This is true so
  `(−1, −1)` is a solution.

Therefore the ordered pairs that are solutions to the inequality
`4x+y > −6` are
`(2, 0) and (−1, −1)`.