Applying the Solving Technique

This page demonstrates the application of the solving steps introduced earlier, providing a detailed walkthrough of solving a set of simultaneous equations.

The example used is: 28 + 2c = 18 38 + 2c = 22

Example: The solving process is shown step-by-step:

1. Subtract 2c from both equations to eliminate the variable c
2. This results in: 28 - 38 = -5 and 18 - 22 = -4
3. Solve for c: 2c = 10, so c = 5

Highlight: The substitution method is implicitly used here, as the value of c is then substituted back into one of the original equations to verify the solution.

This example illustrates how the simultaneous equations solver approach can be applied to real problems, providing students with a clear demonstration of the technique in action.

Definition: Substitution in simultaneous equations involves using the value of one variable found from one equation in the other equation to solve for the remaining variable.

By working through this example, students can see how the abstract steps translate into a practical problem-solving method, reinforcing their understanding of how to solve simultaneous equations step by step.

Understanding Simultaneous Equations

Simultaneous equations are a set of equations that must be solved together to find values that satisfy all equations simultaneously. This page introduces the concept with a practical example and outlines the steps for solving such equations.

Example: The guide presents two simultaneous equations: 5x + 3y = 41 2x + 3y = 20

The solving process begins by identifying common terms between the equations. In this case, the 3y term is present in both equations, which can be used as a starting point for solving.

Highlight: The key to solving simultaneous equations is to manipulate the equations to eliminate one variable, allowing you to solve for the other.

The page outlines six steps for solving simultaneous equations:

1. Cancel out terms
2. Subtract terms
3. Subtract y or x terms
4. Divide the answer by the term's coefficient
5. Multiply the answer by the initial term
6. Cancel out any extra terms

Vocabulary: Elimination method simultaneous equations refers to the process of removing one variable by adding or subtracting equations to simplify the problem.

These steps form the foundation of the elimination method, which is one of the three methods of solving simultaneous equations commonly taught in schools.