Solving Linear Systems by Elimination

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.