Basics Revisited
Equation
An equation is a statement that two mathematical expressions having one or more variables are equal.
Linear Equation
Equations in which the powers of all the variables involved are one are called linear equations. The degree of a linear equation is always one.
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General form of a Linear Equation in Two Variables
The general form of a linear equation in two variables is ax + by + c = 0, where a and b cannot be zero simultaneously.
Representing linear equations for a word problem
To represent a word problem as a linear equation
- Identify unknown quantities and denote them by variables.
- Represent the relationships between quantities in a mathematical form, replacing the unknowns with variables.
Solution of a Linear Equation in 2 variables
The solution of a linear equation in two variables is a pair of values, one for x and the other for y, which makes the two sides of the equation equal.
Eg: If 2x+y=4, then (0,4) is one of its solutions as it satisfies the equation. A linear equation in two variables has infinitely many solutions.
Geometrical Representation of a Linear Equation
Geometrically, a linear equation in two variables can be represented as a straight line.
2x – y + 1 = 0
⇒ y = 2x + 1
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Plotting a Straight Line
The graph of a linear equation in two variables is a straight line. We plot the straight line as follows:
Any additional points plotted in this manner will lie on the same line.
