Question

a number consist of 2 digits whose sum is 11. the number formed by reversing the digit is 9 less than the original number. find the number?​

Answer 1

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a number consist of 2 digits whose sum is 11. the number formed by reversing the digit is 9 less than the original number. find the number?

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Let the tens digit be and the units digit be y. Then the number is 10x+y.

Sum of the digits is x+y=11.

The number formed by reversing the digits is 10y+x.

Given data, (10x+y)−9=10y+x

⇒10x+y−10y−x=9

9x−9y=9

Dividing by 9 on both sides, x−y=1 ........ (2)

Equation (2) becomes x=1+y .......... (3)

Substituting x in (1) we get, 1+y+y=11

⇒2y+1=11

2y=11−1=10

∴y=

2

10

=5

Substituting y=5 in (3) we get, x=1+5=6

∴ The number is 10x+y=10(6)+5=65

Answer 2

Concept:

First order equations include linear equations. In the coordinate system, the linear equations are defined for lines. A linear equation in one variable is one in which there is a homogeneous variable of degree 1 (i.e., only one variable). Multiple variables may be present in a linear equation. Linear equations in two variables, for example, are used when a linear equation contains two variables. Examples of linear equations include 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, and 3x - y + z = 3.

Given:

A number consist of 2 digits whose sum is 11. the number formed by reversing the digit is 9 less than the original number.

Find:

Find the number?​

Solution:

Let the tens digit be and the units digit be y. Then the number is 10x+y.

Sum of the digits is x+y=11.

The number formed by reversing the digits is 10y+x.

Given data, (10x+y)−9=10y+x

⇒10x+y−10y−x=9

9x−9y=9

Dividing by 9 on both sides, x−y=1 ........ (2)

Equation (2) becomes x=1+y .......... (3)

Substituting x in (1) we get, 1+y+y=11

⇒2y+1=11

2y=11−1=10

∴y=10/2=5

Substituting y=5 in (3) we get, x=1+5=6

∴ The number is 10x+y=10(6)+5=65

Therefore, the number is 65

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