Verify that the values of the variables listed are solutions...

Verify that the values of the variables listed are solutions of the system of equations.
$$
\begin{aligned}
&\left\{\begin{array}{r}
{x-y=3} \\
{-3 x+y=1}
\end{array}\right.\\
&x=-2, y=-5 ;(-2,-5)
\end{aligned}
$$

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Key Concepts

System of Linear Equations

A system of linear equations is a collection of two or more equations with a common set of variables, where a solution is a set of values that satisfies all equations simultaneously. This concept is foundational in algebra and applies broadly in various fields for modeling relationships and solving simultaneous constraints.

Solution Verification

Solution verification is the process of substituting the proposed values of variables back into each equation of the system to check for consistency. This step is critical in ensuring that the computed or given solution indeed satisfies all of the original equations, thereby confirming its validity.

Substitution Method

The substitution method involves replacing a variable with a proposed value or an equivalent expression derived from another equation. This technique is not only useful for solving systems of equations but also serves as a means to verify the correctness of a proposed solution by confirming that all equations in the system are satisfied.

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