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.
$$
\begin{aligned}
&\left\{\begin{array}{l}
{2 x+\frac{1}{2} y=0} \\
{3 x-4 y=-\frac{19}{2}}
\end{array}\right.\\
&x=-\frac{1}{2}, y=2 ;\left(-\frac{1}{2}, 2\right)
\end{aligned}
$$

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Key Concepts

System of Linear Equations

A system of linear equations consists of two or more linear equations involving the same set of variables. The goal is to find values for the variables that satisfy all equations simultaneously. This concept is foundational in algebra and appears in many applications across science, engineering, and other fields.

Solution Verification

Solution verification entails substituting the proposed values for the variables into each equation of the system to confirm that all equations are satisfied. This process ensures that the computed or given solution is correct and consistent with the system, which is a crucial step in problem-solving.

Substitution Method

The substitution method involves replacing the variables in an equation with their corresponding values or expressions from another equation. When verifying a solution, this method is useful because it directly tests whether the provided values satisfy the relationships defined by the equations, ensuring the integrity of the solution.

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