FTCE General Knowledge Math Practice Test

What technique is used to combine equations for eliminating a variable?

1. Variable substitution

2. Linear combinations

3. Equations balancing

4. Solution factoring

The correct answer is: Linear combinations

The technique used to combine equations for eliminating a variable is known as linear combinations. This method involves adding or subtracting two or more equations in order to eliminate one of the variables, making it easier to solve the system. By carefully choosing how to combine the equations, you can often simplify the problem and solve for one variable directly before substituting back to find the other. While variable substitution is a valid method for solving systems of equations, it does not specifically focus on combining equations for elimination but rather involves expressing one variable in terms of another. Equations balancing generally pertains to ensuring that an equation remains valid after performing operations, and solution factoring involves rewriting a quadratic or polynomial equation for solving, which is not particularly relevant to the process of eliminating variables in a system of equations. Thus, linear combinations stands out as the most suitable technique for this context.