# Sum of two numbers is 50 and their difference is 10. Find the Numbers.

A system was introduced to define the numbers present from negative infinity to positive infinity. The system is known as the **Number system.** Number system is easily represented on a number line and Integers, whole numbers, natural numbers can be all defined on a number line. The number line contains positive numbers, negative numbers, and zero.

An **equation** is a mathematical statement that connects two algebraic expressions of equal values with ‘=’ sign.

For example: In equation 3x+2 = 5, 3x+ 2 is the left-hand side expression and 5 is the right-hand side expression connected with the ‘=’ sign.

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There are mainly 3 types of equations:

- Linear Equation
- Quadratic Equation
- Polynomial Equation

Here, we will study the Linear equations.

**Linear equations** in one variable are equations that are written as ax + b = 0, where a and b are two integers and x is a variable, and there is only one solution. 3x+2=5, for example, is a linear equation with only one variable. As a result, there is only one solution to this equation, which is x = 3/11. A linear equation in two variables, on the other hand, has two solutions.

A one-variable linear equation is one with a maximum of one variable of order one. The formula is ax + b = 0, using x as the variable.

There is just one solution to this equation. Here are a few examples:

- 4x = 8
- 5x + 10 = -20
- 1 + 6x = 11

Linear equations in one variable are written in standard form as:

ax + b = 0Here,

- The numbers ‘a’ and ‘b’ are real.
- Neither ‘a’ nor ‘b’ are equal to zero.

**Solving Linear Equations in One Variable**

The steps for solving an equation with only one variable are as follows:

**Step 1: **If there are any fractions, use LCM to remove them.

**Step 2:** Both sides of the equation should be simplified.

**Step 3:** Remove the variable from the equation.

**Step 4:** Make sure your response is correct.

**Problem Statement: **The sum of two numbers is 50, and their difference is 10. The task is to find the numbers.

**Solution:**

Let both numbers be first and second.

According to the problem statement:

first + second = 50(Consider this as 1st equation)first – second = 10(Consider this as 2nd equation)

Add both equations:first + second + first – second = 50 + 10

2 * first = 60

first = 60 / 2

first = 30So from this, we get first = 30, put this value in any equation i.e.

first + second = 50 (Put the value of first in this equation)

30 + second = 50

second = 50-30

second = 20So, the numbers are

30and20.If we consider the case i.e.

second – first = 10then the solution will be the same and the first number will become20and the second number will become30.

**Sample Problem: The sum of the two numbers is 20, and their difference is 10. The task is to find the numbers.**

**Solution:**

Let both numbers be first and second.

According to the problem statement:first + second = 20 (Consider this as 1st equation)first – second = 10 (Consider this as 2nd equation)Add both equations:

first + second + first – second = 20 + 10

2 * first = 30

first = 30 / 2

first = 15So from this, we get first = 15, put this value in any equation i.e.

first + second = 20 (Put the value of first in this equation)

15 + second = 20

second = 20-15

second = 5So, the numbers are 15 and 5.

If we consider the case i.e. second – first = 10 then the solution will be the same and the first number will become 5 and the second number will become 15.