4. Linear Equations in Two Variables
- 1. NUMBER SYSTEMS
- 2. A POLYNOMIALS
- 3. COORDINATE GEOMETRY
- 4. LINEAR EQUATIONS IN TWO VARIABLES
- 5. INTRODUCTION TO EUCLID'S GEOMETRY
- 6. LINES AND ANGLES
- 7. TRIANGLES
- 8. QUADRILATERALS
- 9. CIRCLES
- 10. HERON'S FORMULA
- 11. SURFACE AREAS AND VOLUMES
- 12. STATISTICS
- 13. APPENDIX 1: PROOFS IN MATHEMATICS
- 14. APPENDIX 2: INTRODUCTION TO MATHEMATICAL MODELLING
4.1 Introduction - Learning Objectives
4.2 Linear Equations
Example 1:
Write each of the following equations in the form ax + by + c = 0 and indicate the values of a, b and c:
- 2x + 3y = 4.37
- x – 4 = 3y
- 4 = 5x – 3y
- 2x = y
Example 2:
Write each of the following as a linear equation in two variables:
- x = –5
- y = 2
- 2x = 3
- 5y = 2
Exercise 4.1
- The cost of a notebook is twice the cost of a pen. Represent as a linear equation in two variables.
- Express the given equations in ax + by + c = 0 form and identify a, b, c.
4.3 Solution of a Linear Equation
Example 3:
Find four different solutions of the equation x + 2y = 6.
Solutions include: (2,2), (0,3), (6,0), and (4,1)
Example 4:
Find two solutions for each of the following equations:
- 4x + 3y = 12
- 2x + 5y = 0
- 3y + 4 = 0
Exercise 4.2
- Determine the number of solutions y = 3x + 5 has.
- Write four solutions for each of: 2x + y = 7, πx + y = 9, x = 4y
- Check if given points are solutions of x – 2y = 4.
- Find value of k if (2,1) is a solution of 2x + 3y = k.