## Algebra

Linear Equations: 1

**Linear Equations:**

Linear Equations is the easiest of all topics in Algebra and forms the starting point for the study of Algebra. Linear equation is an algebraic equation whose degree is one i.e. the highest exponent of the variable is one. Linear Equations may contain only one variable or more than one variable and is usually associated to solve word problems on the unknown quantities. The graph of a linear equation is simply a straight line that can be depicted on the graph paper. In this lesson we shall try to understand the different types of linear equations based on the number of variables involved with focus on forming equations and solving them. At the end we shall see how to solve special equations on two variables that have only one equation which can have multiple solutions satisfying the equation.

**Linear Equations on One Variable:**** **

The general form a linear equation in one variable is ax+b =0 where a is the coefficient of the variable where a ≠ 0 and b is the constant term.

Solving such an equation, gives a unique value of the variable.

**Example1 :** Six years ago, the age of Tom and Jerry was in the ratio of 5:7 and 12 years from now their ages will be in the ratio of 4:5. What will be their ages 20 years from now?

**Solution:** Let the ages of Tom and Jerry six years ago were 5x and 7x

After 12 years, the age of Tom will be 5x + 6+12 = 5x + 18

Similarly after 12 years, the age of Jerry will be 7x+18

At this point their ages are in the ratio of 4:5, so