Solve the systems using the substitution method. Label each...

Solve the systems using the substitution method. Label each system as consistent or inconsistent. Provide reasons for each step. Check the answer.
$$
\begin{array}{l}
H=3 k+6 \\
2 k+4 H=-4
\end{array}
$$

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Key Concepts

Solution Verification

After obtaining a solution for the system of equations, it is important to substitute the values back into the original equations. This step confirms that the solution is correct and that all equations are satisfied, thereby ensuring the system is solved accurately.

Consistent and Inconsistent Systems

A consistent system is one that has at least one solution, meaning there is at least one set of values for the variables that satisfies all equations. An inconsistent system, on the other hand, has no solutions, implying that the equations contradict each other. Verifying consistency is a critical part of analyzing linear systems.

Substitution Method

The substitution method is a strategy for solving systems of equations where one equation is solved for one variable, and the resulting expression is substituted into the other equation(s). This method reduces the number of variables and simplifies the problem, making it easier to solve for the unknowns.

System of Linear Equations

A system of linear equations is a collection of one or more linear equations involving the same set of variables. The goal is to find all variable values that satisfy every equation in the system simultaneously. Such systems can have a single unique solution, infinitely many solutions, or no solution at all.

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