← GSEB Class 9
Linear Equations in Two Variables
Chapter Overview
A linear equation in two variables x and y is of the form ax + by + c = 0, where a, b, and c are real numbers and a and b are not both zero. The graph of a linear equation is a straight line. Any point on the line represents a solution. Solutions are infinite. The equation can be expressed in the form y = mx + c to find the slope. The chapter covers finding solutions, plotting graphs, equations of lines parallel to axes, and word problems.
Topics Covered
- Linear Equation Definition
- Standard Form ax + by + c = 0
- Graphing Linear Equations
- Finding Solutions
- Slope Concept
- Lines Parallel to Axes
- Word Problems
Key Formulas
ax + by + c = 0 is a linear equation
Line parallel to x-axis: y = k
Line parallel to y-axis: x = k
Every solution (x,y) lies on the line
Real-World Applications
Applications: Economics (supply-demand curves), physics (motion equations), budgeting, business planning.
Study Tips
Tip: Practice plotting graphs carefully
Tip: Find at least three points for each line
Tip: Check solutions by substitution