# Types of Equations

In the above table, we can see that:

- 2x + 1 = 4 is a linear equation with one variable while x + 2 y â€“ 3z = 5 is a linear equation with 3 variables.
- x
^{2}+ 2x + 1 = 0 is a quadratic equation in â€˜xâ€™ and x^{2}+ 2y^{2}â€“ 3x = 5 is a quadratic equation in â€˜xâ€™ and â€˜yâ€™. - The third row contains examples of some cubic equations in 1, 2 and 3 variables.

The highest power (exponent) to which the variable in an equation is raised is known as the **degree of the equation.**

- Linear equation is an equation of degree 1.
- Quadratic equation is an equation of degree 2.
- Cubic equation is an equation of degree 3.

# Linear equations with one variable

An equation of the form ax + b = 0 where x is a variable, a and b are constants and a â‰ 0 is called a linear or simple equation.

The root or solution of the equation ax + b = 0 is given by

If we substitute this value of x in the above equation, the expression on the left hand side will be equal to the expression on the right. Hence, we can tell that satisfies the above equation.

**Example: **6*x* + 12 = 0 is a linear equation with 1 variable.

The root of the above equation will be

Example

Find the value of

*x*ifSolution

Given:

Example

Find the root of the equation

Solution

Given:

Example

The number 50 is split into two parts such that the difference between them is 10. What is the value of smaller part?

Solution

Let us assume one of the parts be

The other part must be what will be left in 50 after taking x, i.e., 50 â€“ x.

Given that the difference between the two parts is 10. Hence,

One part is x = 30.

So, the other part is Hence, the value of the smaller part is 20.

*x*.The other part must be what will be left in 50 after taking x, i.e., 50 â€“ x.

Given that the difference between the two parts is 10. Hence,

One part is x = 30.

So, the other part is Hence, the value of the smaller part is 20.

Example

In a 2 digit number, the digit in tenâ€™s place is thrice the digit in unitâ€™s place. If 36 is subtracted from the number, the digits are reversed. Find the number.

Solution

The digits are unknown; so letâ€™s assume the unitâ€™s place digit be â€˜
Now, as given in the question, digit in tenâ€™s place is thrice which means three times the digit in unitâ€™s place. Thus, tenâ€™s place will be 3x.
When digits are known, the number can be written as:
10 Ã— (digit in tenâ€™s place) + 1 Ã— (digit in unitâ€™s place).
So, the original number will be
When 36 is subtracted, digits are reversed which means the tenâ€™s place will become x and unitâ€™s place will become 3x.
The new number will be 10 Ã— x + 3x = 13x.
From the given condition, 31x â€“ 36 = 13x.

So, we found the value of x as 2, the original number will be 31 Ã— 2 = 62.

*x*â€™.So, we found the value of x as 2, the original number will be 31 Ã— 2 = 62.