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Sum of two numbers is 17 and their difference is 5. What are the numbers?

  • Last Updated : 05 Aug, 2021
Geek Week

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 5x+3 = 7, 5x+ 3 is the left-hand side expression and 7 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. 5x+3=7, for example, is a linear equation with only one variable. As a result, there is only one solution to this equation, which is x = 4/5. 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 = 0

Here,

  • 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 5. What are 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 = 5  (Consider this as 2nd equation)

Add both equations:

first + second + first – second = 17 + 5
2 * first = 22
first = 22 / 2
first = 11

So from this we get first = 11, put this value in any equation i.e.



first + second = 17 (Put the value of first in this equation)
11 + second = 17
second = 17 – 11
second = 6

So, the numbers are 11 and 6.

If we consider the case i.e. second – first = 5, then the solution will be same and the first number will become 6 and second number will become 11.

Sample Questions

Question 1: What two numbers have a sum of 19 and a difference of 15?

Solution:

Let both numbers be first and second. According to the problem statement:

first + second = 19 (Consider this as 1st equation)
first – second = 15  (Consider this as 2nd equation)

Add both equations:

first + second + first – second = 19 + 15
2 * first = 34
first = 34 / 2
first = 17

So from this we get first = 17, put this value in any equation i.e.

first + second = 19 (Put the value of first in this equation)
17 + second = 19
second = 19 – 17
second = 2

So, the numbers are 17 and 2.

If we consider the case i.e. second – first = 15, then the solution will be same and the first number will become 2 and second number will become 17.

Question 2: What two numbers have a sum of 23 and a difference of 13?

Solution:

Let both numbers be first and second.

According to the problem statement: 

first + second = 23 (Consider this as 1st equation)
first – second = 13  (Consider this as 2nd equation)

Add both equations:

first + second + first – second = 23 + 13
2 * first = 26
first = 36 / 2
first = 18

So from this we get first = 18, put this value in any equation i.e.

first + second = 23 (Put the value of first in this equation)
18 + second = 23
second = 23 – 18
second = 5

So, the numbers are 18 and 5.

If we consider the case i.e. second – first = 13, then the solution will be same and the first number will become 5 and second number will become 18.

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