Solving Simultaneous Equations Using the Elimination Method
This page outlines the process of solving simultaneous equations using the elimination method, a crucial technique in algebra. The method is particularly useful for solving simultaneous equations step by step at the GCSE level and beyond.
The elimination method involves several key steps:
- Write down the equations.
- Check whether the signs of the terms are the same or alternate.
- Make the numbers before the variables the same.
- Add or subtract the equations based on the signs from the start.
- Find the value of one variable (x in this case).
- Choose one of the original equations to substitute the found value.
- Substitute the value into the chosen equation to find the other variable (y).
- Write down both values as the solution.
Example: The document provides an example of solving simultaneous equations:
5x + 3y = 26
2x + 5y = 18
The solution process is demonstrated step-by-step, showing how to manipulate the equations to eliminate one variable and solve for both x and y.
Highlight: The method emphasizes the importance of identifying whether the signs of the terms are the same or alternate, as this determines whether you add or subtract the equations.
Vocabulary: Elimination method - A technique for solving simultaneous equations by adding or subtracting equations to eliminate one variable.
Definition: Simultaneous equations - A set of equations with two or more unknowns that must be solved together.
The page also includes visual aids to help students understand the process, such as arrows indicating the steps and annotations explaining key points. This visual approach makes it an excellent resource for those learning how to solve simultaneous equations by substitution or elimination.
Quote: "Use answer to substitute to find y" - This quote emphasizes the final step in the process, where the found value of one variable is used to determine the other.
By mastering this method, students will be well-equipped to tackle a wide range of simultaneous equations examples and answers, from basic to more complex problems. This technique is a fundamental part of algebraic methods for solving systems of equations and is essential for advancing in mathematics studies.