Assessment and Learning in Knowledge Spaces (ALEKS) Practice Exam

What is involved in the substitution method?

1. Using matrices to find solutions

2. Replacing one variable with an equivalent expression containing the other variable

3. Graphing each variable separately

4. Calculating the average of the variables

The correct answer is: Replacing one variable with an equivalent expression containing the other variable

The substitution method involves replacing one variable in an equation with an equivalent expression that contains the other variable. This technique is commonly used in solving systems of equations, particularly when they are expressed in two variables. For instance, if you have a system where one equation is solved for one variable, you can substitute that expression into the other equation. This reduces the number of variables and allows you to solve for one variable at a time. After finding the value for one variable, you can then substitute back to find the value of the other variable. This method is especially effective when one of the equations is already solved for one variable, or can be easily rearranged to do so. By focusing on the relationships between the variables in a systematic way, the substitution method streamlines the problem-solving process.