Question

The difference of two numbers is one. three times the smaller number is two more than twice the larger number. find both numbers?

i need what x equals and what y equals. and i need two equations that you set up to find the two variables

Answer 1

`=>x=5 and y=4`

Explanation:

Let the 2 number be `x and y`

`color(magenta)(=>3y=2x+2` `.........."Eq 1"`

`color(magenta)(=> x-y=1` `............."Eq 2"`

`=>x=y+1`

Substituting `x=y+1` in Eq 1

`=>3y=2(y+1)+2`

`=>3y=2y+2+2`

`=>3y-2y=4`

`color(red)(=>y=4`

Now let us find `x`

`=> x-y=1` [Eq 2]

`=>x-4=1`

`=>x=4+1`

`color(red)(=>x=5`

`color(darkred)("Verification":`

`=>3y=2x+2` [Eq 1]

Replacing `x=5 and y=4`

`=>3*4=2*5+2`

`color(purple)(=>12=12`

And

`=>x-y=1` [Eq 2]

Replacing `x=5 and y=4`

`=>5-4=1`

`color(purple)(=>1=1`

Hence verified!

`therefore` The 2 numbers are `color(darkorange)(4 and 5`

~Hope this helps! :)

Answer 2

`color(blue)(4 , 5 )`

Explanation:

Let the numbers be `x` and `y`, with `x` being the larger number.

Then:

The difference of two numbers is one.

`x-y=1color(white)(8888)[1]`

Three times the smaller number is two more than twice the larger number.

`3y=2x+2color(white)(8888)[2]`

We now solve these simultaneously:

From [1]:

`x=1+y`

Substituting in [2]:

`3y=2(1+y)+2`

`3y=2+2y+2`

`y=4`

Substituting this in `[1]`

`x-4=1`

`x=5`

The two numbers are `4 and 5`