Assessment and Learning in Knowledge Spaces (ALEKS) Practice Exam

When using substitution in a linear equation, what is replaced?

1. A constant with a variable

2. One variable with an equivalent expression

3. The equation with its graph

4. The coefficients of the variables

The correct answer is: One variable with an equivalent expression

When using substitution in a linear equation, one variable is replaced with an equivalent expression. This process involves taking an expression for one variable and inserting it into another equation to simplify or solve the system of equations. For example, if you have a system of equations and one equation is already solved for one variable (like \(x = 2y + 3\)), you can substitute that expression for \(x\) into the other equation. This allows you to work with only one variable at a time, making it easier to find the solution to the system. The other options, while they may involve changes within mathematical processes, do not accurately describe the process of substitution in the context of a linear equation. Replacing a constant with a variable or the coefficients of the variables doesn't reflect the nature of substitution. Likewise, substituting the equation with its graph pertains more to visual representation rather than manipulating the algebraic forms of the equations themselves. Thus, the focus on replacing one variable with an equivalent expression is a fundamental principle in the process of substitution in linear equations.