Practice Problems and Advanced Techniques
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:
- Multiply the first equation by 5 and the second by 2
- Subtract the resulting equations to eliminate y
- Solve for x
- 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:
- 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.
