Question

Which of the following would be a possible solution to the system of inequalities given below?

(3,-3)
(1,-7)
(6,4)
(-5,0)

Answer 1

(3, -3)

Explanation:

A point qualifies as a solution to a system of inequalities if it is true when both of its x and y values are substituted into the both inequalities. Knowing this, let's plug in the first option, (3, -3), into both inequalities.

Let's try 6x + 3y > 3 first. Substitute 3 for x and -3 for y:

`6 (3) + 3 (-3) > 3\\18 - 9 > 3\\9 > 3`

9 is bigger than 3, so (3, -3) is a solution to that inequality.

Let's try
`x -y \geq 4`. Do the same, substituting the same values:

`3 - (-3) \geq 4\\3 + 3 \geq 4\\6\geq 4`

6 is bigger than 4, so (3, -3) is a solution to that inequality too.

Since (3, -3) is a solution to both inequalities, it must be the answer.