Linear equation in one variable
When an equation has only one variable of degree one, then that equation is known as linear equation in one variable.
- Standard form: ax+b=0, where a and b ϵ R & a ≠ 0
- Examples of linear equation in one variable are :
– 3x-9 = 0
– 2t = 5
Linear equation in 2 variables
When an equation has two variables both of degree one, then that equation is known as linear equation in two variables.
Standard form: ax+by+c=0, where a, b, c ϵ R & a, b ≠ 0
Examples of linear equations in two variables are:
Examples of Linear Equations
The solution of linear equation in 2 variables
A linear equation in two variables has a pair of numbers that can satisfy the equations. This pair of numbers is called as the solution of the linear equation in two variables.
- The solution can be found by assuming the value of one of the variable and then proceed to find the other solution.
- There are infinitely many solutions for a single linear equation in two variables.
Graph of a 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 in the form (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.
Solutions of Linear equation in 2 variables on a graph
- 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 passing through the origin
- Certain linear equations exist such that their solution is (0,0). Such equations when represented graphically pass through the origin.
- The coordinate axes namely x-axis and y-axis can be represented as y=0 and x=0, respectively.
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.