Question

Indicate whether (4, 12) is a solution of the given system.
y ≤ x
y > x + 3

Answer 1

not a solution

Explanation:

You want to know if (4, 12) is a solution to the system of inequalities y ≤ x and y > x+3.

Test

Using the offered values in the first inequality, we get ...

y ≤ x . . . . for (x=4, y=12)

12 ≤ 4 . . . . . false

The given point does not satisfy the inequality, so is not a solution.

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Additional comment

The attached graph shows there are no solutions to the system. (The solution regions do not overlap.)

It should be clear from an arithmetic point of view that x+3 is greater than x. It is impossible for y to be both greater than x and less than x at the same time.