Question

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

Answer 1

Answer:

(3, -3)

Step-by-step 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.