Question

The sum of two numbers is 10 and the difference of them is 2. Then the greater number of these two is ______

Answer 1

Hint: We assign two different variables to two numbers and form two equations each form sum of two numbers and for difference of two numbers. Use a substitution method to find the value of one variable in terms of another and calculate the value of numbers.
* Sum of two numbers ‘a’ and ‘b’ is given by \[a + b\]
* Difference of two numbers ‘a’ and ‘b’ is given by \[a - b\]

Complete step-by-step solution:
Let us assume two number ‘x’ and ‘y’
We are given that the sum of two numbers is 10.
We form an equation of sum of two numbers ‘x’ and ‘y’ and equate it to the value 10
\[ \Rightarrow x + y = 10\],,,,,,,,,,,,,,,,,,… (1)
We are given that the difference of two numbers is 2.
We form an equation of difference of two numbers ‘x’ and ‘y’ and equate it to the value 2
\[ \Rightarrow x - y = 2\]...................… (2)
We use substitution method to solve for the values of ‘x’ and ‘y’ from equations (1) and (2)
From equation (1):\[x + y = 10\]
Shift one of the variables (say ‘x’) to right hand side of the equation
\[ \Rightarrow y = 10 - x\] ………………..… (3)
Substitute the value of ‘y’ from equation (3) in equation (2)
\[ \Rightarrow x - (10 - x) = 2\]
Open the bracket in left hand side of the equation
\[ \Rightarrow x - 10 + x = 2\]
Add like terms in left hand side of the variable and shift all constants to right hand side of the equation
\[ \Rightarrow 2x = 2 + 10\]
\[ \Rightarrow 2x = 12\]
Divide both sides of the equation by 2
\[ \Rightarrow \dfrac{{2x}}{2} = \dfrac{{12}}{2}\]
Cancel same factors from numerator and denominator on both sides of the equation
\[ \Rightarrow x = 6\]
Substitute the value of ‘x’ in equation (3)
\[ \Rightarrow y = 10 - 6\]
\[ \Rightarrow y = 4\]
\[\therefore \]Two numbers having sum 10 and difference 2 are 6 and 4.
Since \[6 > 4\]

\[\therefore \]Greater number of the two numbers 6 and 4 is 6

Note: Students many times make mistakes when shifting values from one side of the equation to another, keep in mind we always change sign from positive to negative and vice-versa when shifting values to the opposite side of the equation. Also while checking which number is greater or smaller we can use the concept of number line, the number lying on the right hand side of another number is always greater than the number on the left.
We use linear equations in one variable when there is one unknown variable. We use linear equations in two variables when there are two unknown variables.