Which action is least effective when solving a simple system of two linear equations quickly?

Which action is least effective when solving a simple system of two linear equations quickly?

• A. Using elimination
• B. Substituting
• C. Graphing the equations to find an exact intersection
• D. Factoring the equations (not applicable)

Answer: (D)

In quick solving of a simple two-variable linear system, you want a method that directly uses the equations to isolate a variable or cancel terms. Two fast, standard approaches are elimination, which adds or subtracts equations to cancel one variable and reveal the other, and substitution, which solves one equation for one variable and plugs that expression into the other. Graphing can work when the intersection is easy to read, but it often lacks precision and can take longer by hand. Factoring, on the other hand, isn’t a technique used for solving linear systems. Factoring is a tool for polynomial expressions, used to find zeros or simplify, but two linear equations are already in their simplest linear form. There isn’t a straightforward way to factor them to obtain the solution, so this approach doesn’t fit and won’t lead to a quick result. That’s why factoring is the least appropriate method for solving this kind of problem.

In quick solving of a simple two-variable linear system, you want a method that directly uses the equations to isolate a variable or cancel terms. Two fast, standard approaches are elimination, which adds or subtracts equations to cancel one variable and reveal the other, and substitution, which solves one equation for one variable and plugs that expression into the other. Graphing can work when the intersection is easy to read, but it often lacks precision and can take longer by hand.

Factoring, on the other hand, isn’t a technique used for solving linear systems. Factoring is a tool for polynomial expressions, used to find zeros or simplify, but two linear equations are already in their simplest linear form. There isn’t a straightforward way to factor them to obtain the solution, so this approach doesn’t fit and won’t lead to a quick result. That’s why factoring is the least appropriate method for solving this kind of problem.