What is a common mathematical technique used to solve systems of linear equations?

• A. Substitution or elimination methods.
• B. Graphing only.
• C. Power rules.
• D. Factoring polynomials.

Answer: (A)

Solving systems of linear equations by combining the equations to eliminate or substitute variables is a standard, reliable method. Substitution works by solving one equation for one variable and plugging that expression into the other equation, which gives an exact value for each variable. Elimination achieves the same goal by adding or subtracting a multiple of one equation from the other to cancel a variable, leaving a single-variable equation to solve. For example, with x + y = 5 and x - y = 1, adding the equations gives 2x = 6, so x = 3, and then y = 2. This approach consistently yields exact solutions for any pair of linear equations.

Graphing can show where the lines meet, but it often provides only an approximate solution and isn’t as precise or algebraic as substitution or elimination. Power rules apply to exponents, not solving systems of equations. Factoring polynomials is a technique for single-variable polynomial equations, not the standard way to handle linear systems.