This page focuses on the elimination method in algebra for solving systems of linear equations, providing a step-by-step guide and examples.

The elimination method consists of four main steps:

1. Multiply one or both equations to create opposite coefficients for one variable
2. Add the equations to eliminate one variable
3. Solve for the remaining variable
4. Substitute the value found in step 3 into either original equation to solve for the other variable

Highlight: The elimination method is particularly effective when coefficients can be easily manipulated to cancel out a variable.

Three examples demonstrate the application of the elimination method:

Example 1 solves: 4x + 5y = 3 -3x + 2y = 38

Example 2 addresses: 5x - 3y = 35 8x + 2y = 22

Example 3 presents a word problem about purchasing throw blankets with embroidered letters, showing how to apply the elimination method to practical situations.

Example: In the throw blanket problem, students learn to set up equations based on given information: x + 6y = 29 and x + 3y = 24.50, where x represents the cost of the blanket and y represents the cost per letter.

Vocabulary: Elimination method - A technique for solving systems of equations by adding or subtracting equations to cancel out one variable.

The page concludes with the solution to the word problem, demonstrating how to interpret the mathematical results in the context of the original question about blanket and embroidery costs.

This page introduces the substitution method for solving linear systems and provides detailed examples to illustrate the process.

The substitution method involves three key steps:

1. Solve one equation for one variable
2. Substitute the expression into the other equation and solve for the remaining variable
3. Use the value found in step 2 to solve for the final variable

Highlight: The substitution method is particularly useful when one equation is already solved for a variable or can be easily rearranged.

Three examples are provided to demonstrate the application of the substitution method:

Example 1 solves the system: x + y = 3 3x + y = -1

Example 2 tackles: x - y = -4 2x + y = 4

Example 3 presents a word problem involving ticket sales at a comedy club, demonstrating how to apply the substitution method to real-world scenarios.

Example: In the comedy club problem, students learn to set up equations based on given information: 68x + 136y = 1088 and 79x + 140y = 1183, where x represents adult ticket price and y represents student ticket price.

Vocabulary: Linear system - A set of two or more linear equations with the same variables.

The page concludes with the solution to the word problem, illustrating how to interpret the mathematical results in the context of the original question.