# Linear Equations in Two Variables - Class 9 : Notes

(1) An equation of the form $ax + by + c = 0$, where a, b, c are real numbers such that a and b not both zero is called a linear equation in two variables.
For Example:Â $2x + 3y + 5 = 0$, where $a = 2$, $b = 3$ which are not zero. So this is linear equation in two variables.

(2) A linear equation in two variables has infinitely many solutions.
For Example:Â we have $4x - y - 3 = 0$, there is many solution
If we take $x = 1$ , $y = 1$ then $LHS = 4 \times 1 - 1 - 3 = 0 = RHS$
If we take $x = 2$ , $y = 5$ then $LHS = 4 \times 2 - 5 - 3 = 0 = RHS$

(3) The graph of a linear equation in two variables is a straight line.
For Example:
$x + y = 4$
We have $x + y = 4 \Rightarrow y = 4 - x$
When $x = 0$, we have: $y = 4 - 0 = 4$
When $x = 2$, we have: $y = 4 - 2 = 2$
When $x = 4$, we have: $y = 4 - 4 = 0$
Thus, we have the following table:Plotting the points (0, 4) (2, 2) and (4, 0) on the graph paper and drawing a line joining them.

(4) The equations of x and y-axes are $y = 0$ and $x = 0$ respectively.
For Example:
$x + 3 = 0$ equation is for x-axes because in this equation $y = 0$.
$7y - 3 = 0$Â equation is for y-axes because in this equation $x = 0$.

(5) The graph of the equation $x = a$ is a straight line parallel to y-axis.
For Example:
The equation for such a line $x = - {9 \over 2}$ is given below:

(6) The graph of the equation $y = a$ is a straight line parallel to x-axis.
For Example:Â For a line that is parallel to the x-axis, the equation for such a line $y = 2$ is given below:

(7) Every point on the graph of a linear equation in two variables is a solution of the equation. Conversely, every solution of linear equation in two variables represents a point on the graph of the equation.
For Example:Â In linear equation $f(x) = x + 2y - 1 = 0$ , $\left( {3, - 1} \right)$ also lies on this line.

• Anonymous

Good... But need more explanation

• THIS ALL ARE WRITTEN IN THE BOOKS, YOU SHOULD MAKE THE STUDENT UNDERSTAND, JUST BY COPYING FORMULAS N IS NOT A WAY TO UNDERSTAND

OOOOOOOOO

• Ananya Sarkar

• anushka

explanation could be better ...way better

• Thanx

• Javeriya

Nice app to learn

• good

• Kavya gupta

*******OSSOUM *******