Determining Solutions of Linear Equations in Two Variables

Vocabulary and core concepts covering how to verify whether given ordered pairs are solutions to a linear equation.

Solution to a linear equation

An ordered pair $(x, y)$ that results in a true statement (such as $8 = 8$) when its coordinates are substituted into the equation.

Ordered pair

A coordinate pair written in the form $(x, y)$, such as $(2,2)$, $(-1,3)$, or $(-2,-2)$, representing values to evaluate in an equation.

Substitution method for testing ordered pairs

The procedure of replacing variable $x$ with the first coordinate and variable $y$ with the second coordinate of an ordered pair to check whether the equation remains balanced.

Evaluation of $(2,2)$ for $x + 3y = 8$

Substituting $2$ for $x$ and $2$ for $y$ produces $2 + 3(2) = 8$, which simplifies to $2 + 6 = 8$ and $8 = 8$, verifying that the ordered pair is a solution.