Determine whether the given ordered pair is a solution of the given system. (2,-3) x+y=-1 2 x+5

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Determine whether the given ordered pair is a solution of...

Key Concepts

Systems of Linear Equations

A system of linear equations consists of two or more equations involving the same set of variables. The goal is to find the values of these variables that simultaneously satisfy all the equations. These systems form the basis for many concepts in algebra and are solved using a variety of methods including graphing, substitution, elimination, and matrix operations.

Ordered Pair

An ordered pair represents a set of two elements, typically corresponding to the values of two variables in a coordinate system. In the context of a system of two equations, an ordered pair (x, y) is a candidate solution, and the pair is considered a valid solution only if it satisfies each equation in the system.

Verification of Solutions

Verification involves substituting the values from a potential solution, such as an ordered pair, into each equation of the system to check if the equations hold true. This step is critical because it confirms whether the candidate indeed satisfies the conditions imposed by every equation in the system.

Substitution Method

The substitution method involves replacing a variable with a specific value or an expression from another equation. When a potential solution is provided, the substitution method is used to plug in the values of the variables into the system's equations to determine if the resulting statements are correct, thereby confirming the validity of the solution.

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