Question

The sum of two numbers is 15 and the difference is 5 . What is the number ?
Explain in briefly​

Answer 1

let the numbers be x and y

therefore, x+y =15---i)

x-y=5-----ii)

(x+y) + (x-y) = 15+5

x+y+x-y = 20

x+x = 20

x= 10

when x= 10,

10+y= 15

y=15-10

y= 5

x is 10 and y is 5 :)..

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Answer 2

Linear equations

While solving these types of questions, always keep in mind the concepts listed below:

• The concept of linear equations and solving of linear equations using numerical method.

• The concept of linear equations in two variable.

We know the linear equations in two variable is in the form of $ax + by = 0.$ Which have only two variable that is called Linear equations in two variable. Our question is also related to this topic.

So here we are stated that, The sum of two numbers is 15 and the difference is 5. With this information, we've been asked to find out that unknown numbers.

Let's suppose that $x$ and $y$ be the unknown numbers respectively.

So our equation equation would be like this;

$\implies x + y = 15 \qquad .... .... (1)$

$\implies x - y = 5 \qquad .... .... (2)$

Now we have two equations. By adding equation (1) and equation (2) we get:

$\implies (x + y) + (x - y) = 15 + 5 \\ \\ \implies x+y+x-y = 20 \\ \\ \implies x + x + y - y = 20 \\ \\ \implies x + x = 20 \\ \\ \implies 2x = 20 \\ \\ \implies x =\cancel \dfrac{20}{2} \\ \\ \implies \boxed{x = 10}$

Now we got the value of x, by putting the value of x in equation (1) we get:

$\implies 10 + y = 15 \\ \\ \implies y = 15 - 10 \\ \\ \implies \boxed{y = 5}$

Therefore, the unknown numbers is 10 and 5 respectively.