# CBSE 9th Maths

## Linear Equations in Two Variables

### linear equation in 2 variables:

1. Linear Equations: Any equation which can be put in the form ax + by + c = 0, where a, b and c are real numbers and a and b are not both zero is called a linear equation in two variables.
The solution of a linear equation is not affected when

• the same number is added to (or subtracted from) both the sides of the equation.
• you multiply or divide both the sides of the equation by the same non-zero number.
2. A linear equation in two variables has infinitely many solutions.
3. The graph of every linear equation in two variables is a straight line.
4. x = 0 is the equation of the y-axis and y = 0 is the equation of the x-axis.
5. The graph of x = a is a straight line parallel to the y-axis.
6. The graph of y = a is a straight line parallel to the x-axis.
7. An equation of the type y = mx represents a line passing through the origin.
8. Every point on the graph of a linear equation in two variables is a solution of the linear equation. Moreover, every solution of the linear equation is a point on the graph of the linear equation.

### Graphical representation of a linear equation in 2 variables:

• Any linear equation in the standard form ax+by+c=0 has a pair of solutions (x,y), that can be represented in the coordinate plane.
• When an equation is represented graphically, it is a straight line that may or may not cut the coordinate axes. • A linear equation ax+by+c=0 is represented graphically as a straight line.
• Every point on the line is a solution for the linear equation.
• Every solution of the linear equation is a point on the line.

### Lines parallel to coordinate axes

• Linear equations of the form y=a, when represented graphically are lines parallel to the x-axis and a is the y-coordinate of the points in that line.
• Linear equations of the form x=a, when represented graphically are lines parallel to the y-axis and a is the x-coordinate of the points in that line. 