# Sum of two numbers is 17 and their difference is 7. 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 4x+2 = 8, 4x+ 2 is the left-hand side expression and 8 is the right-hand side expression connected with the ‘=’ sign.

There are mainly 3 types of equations:

- Linear Equation
- Quadratic Equation
- Polynomial Equation

Here, we will study about 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 = 1. 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.

### Sum of two numbers is 17 and their difference is 7. Find the numbers.

**Solution:**

Let both numbers be first and second.

According to the problem statement:

first + second = 17 (Consider this as 1st equation)first – second = 7 (Consider this as 2nd equation)Add both equations:

first + second + first – second = 17 + 7

2 * first = 24

first = 24 / 2

first = 12So from this we get first = 12, put this value in any equation i.e.

first + second = 17 (Put the value of first in this equation)

12 + second = 17

second = 17 – 12

second = 5

So, the numbers are 12 and 5.If we consider the case i.e. second – first = 7, then the solution will be same and the first number will become 5 and second number will become 12.

**Sample Questions**

**Question 1: The sum of two numbers is 20, and the difference between the two numbers 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 = 5

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

**Question 2: What two numbers have a sum of 9 and a difference of 5?**

**Solution:**

Let both numbers be first and second.

According to the problem statement:

first + second = 9 (Consider this as 1st equation)first – second = 5 (Consider this as 2nd equation)Add both equations:

first + second + first – second = 9 + 5

2 * first = 14

first = 14 / 2

first = 7So from this we get first = 7, put this value in any equation i.e.

first + second = 9 (Put the value of first in this equation)

7 + second = 9

second = 9 – 7

second = 2

So, the numbers are 7 and 2.If we consider the case i.e. second – first = 5, then the solution will be same and the first number will become 2 and second number will become 7.