Substitution

Substitution is a method used in algebra to simplify and solve equations. It involves replacing a variable with a known value or expression. This technique is particularly useful when dealing with complex or multi-step equations.

How to Use Substitution

When using substitution, follow these steps:

1. Identify the variable: Determine which variable in the equation you want to replace.
2. Express the variable: Express the variable in terms of another variable or a known value.
3. Replace the variable: Substitute the expression from step 2 for the identified variable in the original equation.
4. Solve for the remaining variable: Use the substituted equation to solve for the remaining variable.
5. Check your solution: Verify the solution by substituting the values back into the original equation.

Example

Let's consider the equation 3x + 2y = 10 and y = 2x - 1. We can use substitution to solve for x and y.

First, we express y in terms of x using the given equation: y = 2x - 1.

Next, we substitute 2x - 1 for y in the original equation: 3x + 2(2x - 1) = 10.

Solving the equation gives us the value of x. After finding x, we can substitute its value back into y = 2x - 1 to find the value of y.

Study Guide

To master the concept of substitution, follow these study tips:

• Understand the concept: Familiarize yourself with the idea of replacing variables with known values or expressions.
• Practice solving equations: Work on various substitution problems to gain proficiency in the method.
• Identify the variable to substitute: Learn to recognize which variable to replace in a given equation.
• Check your solutions: Always double-check your solutions by substituting the values back into the original equation to ensure accuracy.

By practicing these steps and tips, you can become proficient in using substitution to solve algebraic equations.