Is (x, y) a solution to the system of equations?

Learning Objectives Define what a solution to a single linear equation represents. Define what a solution to a system of linear equations represents. Accurately substitute the x and y values from an ordered pair into a linear equation. Determine if a given ordered pair (x, y) satisfies a single linear equation. Determine if a given ordered pair (x, y) satisfies *all* equations in a system of linear equations. Explain why a point must satisfy every equation to be considered a solution to the entire system. Ever wonder if a secret code works for *all* parts of a message? 🕵️‍♀️ In math, we'll learn how to check if a single point works for *all* equations in a system! This lesson will teach you how to verify if a specific point (x, y) is a solution to a system of linear eq...

TermDefinitionExample Linear EquationAn equation whose graph is a straight line. It typically involves two variables, like x and y, and no variable is raised to a power higher than 1.$2x + y = 5$ Ordered Pair (x, y)A pair of numbers written in a specific order, usually representing a point on a coordinate plane. The first number is the x-coordinate, and the second is the y-coordinate.$(3, -1)$ where $x=3$ and $y=-1$ Solution to a Single EquationAn ordered pair (x, y) that makes the equation true when its values are substituted for the variables.For $x + y = 7$, the point $(3, 4)$ is a solution because $3 + 4 = 7$ is true. System of Linear EquationsTwo or more linear equations that are considered together. We are looking for a solution that satisfies *all* of them at the same time.$\{ \beg...

Rule for Checking a Single Linear Equation Given an equation $Ax + By = C$ and an ordered pair $(x_0, y_0)$, substitute $x_0$ for $x$ and $y_0$ for $y$. If $A(x_0) + B(y_0) = C$ is a true statement, then $(x_0, y_0)$ is a solution to that equation. Use this rule to determine if a point lies on the line represented by a single equation. The goal is to see if the left side of the equation equals the right side after substitution. Rule for Checking a System of Linear Equations Given a system of equations and an ordered pair $(x_0, y_0)$, substitute $x_0$ for $x$ and $y_0$ for $y$ into *each* equation in the system. If $(x_0, y_0)$ makes *all* equations true, then it is a solution to the system. If it makes even one equation false, it is NOT a solution to the system. This is the...