1Cademy - Determining Whether Ordered Pairs are Solutions of $$y = 2x

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Solution of a Linear Equation in Two Variables

Example

Determining Whether Ordered Pairs are Solutions of $y = 2x - 3$

To determine whether ordered pairs satisfy the equation $y = 2x - 3$ and lie on its graph, substitute the $x$ and $y$ coordinates into the equation and examine the resulting statement. - For $(0, -3)$ : $-3 = 2(0) - 3 \implies -3 = -3$ . This is a true statement, so $(0, -3)$ is a solution. When plotted, it lies on the line $y = 2x - 3$ . - For $(3, 3)$ : $3 = 2(3) - 3 \implies 3 = 3$ . This is a true statement, so $(3, 3)$ is a solution and lies on the line. - For $(2, -3)$ : $-3 = 2(2) - 3 \implies -3 = 1$ . This is a false statement, so $(2, -3)$ is not a solution, and the plotted point does not lie on the line. - For $(-1, -5)$ : $-5 = 2(-1) - 3 \implies -5 = -5$ . This is a true statement, so $(-1, -5)$ is a solution and lies on the line. This confirms the core principle linking linear equations and their graphs: points that are solutions to the equation are located precisely on its line, while points that are not solutions fall outside the line.

Updated 2026-04-23

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OpenStax Intermediate Algebra

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