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

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  • Last Updated : 05 Aug, 2021

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 = 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 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 = 12

So 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 = 15

So 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 = 7

So 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.

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