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Solution to a Linear Inequality in Two Variables

Example

Determining Whether Ordered Pairs Are Solutions of $y > x + 4$

To determine if specific ordered pairs satisfy the linear inequality $y > x + 4$ , substitute the respective $x$ and $y$ coordinates into the expression. If the resulting mathematical statement is true, the pair is a solution; if false, it is not. Testing the given points:

For $(0, 0)$ : Substituting $x = 0$ and $y = 0$ yields $0 > 0 + 4$ , which simplifies to $0 > 4$ . This is false, so $(0, 0)$ is not a solution.
For $(1, 6)$ : Substituting $x = 1$ and $y = 6$ yields $6 > 1 + 4$ , which simplifies to $6 > 5$ . This is true, so $(1, 6)$ is a solution.
For $(2, 6)$ : Substituting $x = 2$ and $y = 6$ yields $6 > 2 + 4$ , which simplifies to $6 > 6$ . This is false, so $(2, 6)$ is not a solution.
For $(-5, -15)$ : Substituting $x = -5$ and $y = -15$ yields $-15 > -5 + 4$ , which simplifies to $-15 > -1$ . This is false, so $(-5, -15)$ is not a solution.
For $(-8, 12)$ : Substituting $x = -8$ and $y = 12$ yields $12 > -8 + 4$ , which simplifies to $12 > -4$ . This is true, so $(-8, 12)$ is a solution.

Updated 2026-05-06

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