This page builds upon the previous concepts by presenting more complex simultaneous equations and their solutions. It also introduces practice problems to reinforce learning.

The page starts with a set of equations: 3x + 2y = 17 2x + 5y = 4

It demonstrates the solution process using the elimination method:

1. Multiply the first equation by 5 and the second by 2
2. Subtract the resulting equations to eliminate y
3. Solve for x
4. Substitute x back into one of the original equations to solve for y

Example: 15x + 10y = 85 4x + 10y = 8 Subtracting these equations eliminates y: 11x = 77 x = 7

The page then provides practice problems for students to solve:

1a) 7b + 3g = 136 2b + 2g = 86

1b) 5b + 4g = 215 15b + 12g = 645

Highlight: These practice problems are designed to help students apply the techniques for balancing equations in math that they've learned.

The solutions to these problems are also provided, showing the step-by-step process for each. This reinforces the importance of methodical problem-solving in algebra.

Definition: Elimination method - A technique for solving simultaneous equations by adding or subtracting equations to remove one variable, allowing for the solution of the remaining variable.

The page concludes with more complex equations, encouraging students to apply their knowledge to increasingly challenging problems:

2. 4x + 5y = -3 6x - 2y = 25

This final example demonstrates how to handle equations with negative numbers and fractions, further expanding students' understanding of solving simultaneous equations step by step.

This page introduces the concept of simultaneous equations and demonstrates various solving methods. It provides a detailed walkthrough of solving different types of equations, emphasizing the step-by-step approach.

The page begins with a set of simultaneous equations: 3y + 2x = 12 3x = 5

It then proceeds to show the solution process, which involves manipulating the equations to isolate variables. The method demonstrated here is the substitution method, where one equation is rearranged to express one variable in terms of the other.

Example: 3x = 5 x = 5/3

This value of x is then substituted into the other equation: 3y + 2(5/3) = 12

The solution continues by solving for y: 3y = 12 - 10/3 3y = 26/3 y = 26/9

The page also includes other examples of simultaneous equations with different complexities: 15y + 6x = 36 8y - 6x = 10

These equations are solved using the elimination method, where equations are added or subtracted to eliminate one variable.

Highlight: The page emphasizes the importance of showing all steps clearly, which is crucial for understanding complex algebraic expressions.

Vocabulary: Simultaneous equations - A set of equations involving the same variables that must be solved together to find values that satisfy all equations simultaneously.