Some important points to revise from the chapter are: • An equation of the form ax + by + c = 0, where a, b and c are real numbers, such that a and b are not both zero, is called a linear equation in ...

In this video we will learn about the plotting of graphs for a pair of linear equations in two variables. Two straight lines are obtained when we plot a pair of linear equations on the graph paper ...

Show values that satisfy an inequality on a set of axes by drawing the line of the corresponding equation and shading the area specified in a question. Include a dashed line for inequalities where the ...

Linear functions are fundamental building blocks in mathematics and play a key role in solving real-world problems where the rate of change remains constant. Linear functions arise in a wide range of ...

Simultaneous linear equations are used to model situations where two relationships must be satisfied at the same time. These problems often involve two interdependent variables, such as comparing ...

ABSTRACT: This paper presents a new dimension reduction strategy for medium and large-scale linear programming problems. The proposed method uses a subset of the original constraints and combines two ...