Test whether a point satisfies an inequality. | Linear inequalities in one or two variables | SAT Math

Check whether a point belongs to an inequality’s solution set by substitution.

Core Idea

Substitute the point's coordinates into the inequality — if the resulting statement is true, the point is in the solution set.

Understanding

Testing a point is the most direct way to check whether it belongs to the solution region of an inequality. Plug the $𝑥$ - and $𝑦$ -values into the inequality and simplify. If you get a true statement (like $2 < 5$ ), the point satisfies it. If false (like $7 < 5$ ), it doesn't.

This technique is useful in two situations: verifying your own graph by checking a point you know should be in or out, and answering SAT questions that ask "which point satisfies the inequality" or "which inequality is satisfied by the point."

When a system of inequalities is involved, the point must satisfy every inequality in the system to be in the feasible region.

Step by Step

Substitute the x-coordinate and y-coordinate of the point into the inequality.
Simplify both sides.
Check whether the resulting numerical statement is true or false.

Misconceptions

Mixing up x and y when substituting — always match each coordinate to the correct variable.
Forgetting that a point on a dashed boundary line does NOT satisfy a strict inequality (< or >).

Question

Worked Example

Which point lies in the solution set of $2 𝑥 + 5 𝑦 < 20$ ?

Select an answer to see the explanation