Question

6.) The sum of two numbers is 45.

The larger number y is 6 less than twice the smaller number
a.
Write a system of linear equations.
What is the smaller number?

Answer 1

x= 13 =smaller number

Explanation:

let x=smaller number

y=2x-6=larger number

x+y=45

x+2x-6=45 (equation)

3x=39

x=13

Answer 2

`x = 13` ..... smaller number

and

`y = 32` ....... larger number

Explanation:

Greetings!!!

Let the two numbers be X and Y

`x + y = 45........ \:equation \: 1`

The larger number is y and is 6 less than twice the smaller number. which means:-

`(y - 6) = 2x........... \: equation \: 2`

so, now solve for y. from equation 2

`y - 6 = 2x \\ y = 2x + 6`

Substitute equation 1 into equation 2

`x + y = 45 \\ x + (2x + 6) = 45 \\ 3x + 6 = 45 \\ 3x = 45 - 6 \\ 3x = 39....divide \: both \: sides \: by \: 3 \\ x = 13`

To solve for y substitute x into the first equation

`(13) = + y = 45 \\ y = 45 - 13 \\ y = 32`

Finally, to be more sure make a cross check

`y - 6 = 2x \\ 32 - 6 = 2(13) \\ 26 = 26`

If you have any questions tag it on comments

Hope it helps!!!