Linear equation and Linear inequality are differentiatable on the sybolically. The symbol used in linear equation is "=" equality sign and the symbols used in linear inequality are ">","<","
"≤", " ≥".
We need to distinguish between linear inequalities in two variables and systems of linear equations in two variables.
We will first discuss linear equations and then linear inequalities.
Linear Equations:
If a equation is written in the form ax + by + c=0, the equation is said to be a linear equation in two variables. where a, b & c are real numbers and coefficients of x and y. , that is, a and b are not equal to zero.
Characterstic :
- Variables in a linear equation are not raised to powers or used as denominators of fractions
- Find pairs of values that make the linear equation true, and plot those pairs on a coordinate grid so that all points are Lying on the same line. The graph of a linear equation is a straight line.
- A linear equation in two variables can be written as a linear relationship between x and y.
For example, 10x+4y = 3 and -x+5y = 2 are linear equations in two variables.
methods for solving linear equations in two variables:
- graphical methods
- replacement methods
- cross-multiplication methods
- elimination methods
Linear inequality:
Linear inequalities in two variables use the greater than (>), less than (<), greater than or equal to (≥), and less than or equal to (≤) symbols instead of the equal (=) symbol. Use the.
Features:
- You can add, subtract, multiply and divide with the same number to solve inequalities
- Multiply and divide with negative numbers reverse the inequality
- Order outside shaded area Pairs are inequalities that cannot be solved graphically.
Example: 8x + 3y ≥ 5 and 2x + 3y < 10 are linear inequalities in two variables.
Method: Graphical
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