Math: Linear Equations in Two Variables Class 10

Math: Linear Equations in Two Variables Class 10

Linear equations in two variables represent a plane in three dimensions. They can also represent lines passing through a single point. The general form of a linear equation in two variables is Ax + By = C. In this context, A, B, and C are constants, while x and y are variables. Linear equations can have infinite solutions when graphed.

Solving Linear Equations in Two Variables

Solving a linear equation involves finding its roots (x and y values), which define the points where it intercepts the coordinate axes. There are several ways to solve linear equations, including substitution, elimination, cross multiplication, and graphical methods. For example, consider the following system of equations:

y = mx + c (line equation) x + y = n (point equation)

To find the intersection point of these lines, we need to equate them:

mx + c = x + y - n mx = x + y - c x(m - 1) + y = c

This equation can help us find the intersection point between the line equation and the point equation.

Applications of Linear Equations

Linear equations in two variables have numerous applications in real life. One common application is in economics, where demand and supply functions are often represented by linear equations. Other applications include calculating distances, determining rates, analyzing costs, modeling relationships, and solving problems involving percentages.

In conclusion, understanding linear equations in two variables is crucial for various mathematical and real-life applications. It allows us to model and analyze situations with multiple variables, making it an essential part of our mathematical toolkit.