Linear system: equation with variables

The sum of two integers is 38. Four times the smaller is 65 less than three times the larger. Find the numbers.

(practice questions for exam =| )

let the two integers be X and Y
given,
X+Y=38................(1)
let X be the smaller of the two
then,
4X=3Y-65
4X-3Y=-65............(2)

SOLVE 1 AND 2

multiply (1)by 3
3X+3Y=114
4X-3Y=-65

SO, 7X=49
X=7

from 1,
X+Y=38
7+Y=38
Y=31

One Number = x
Other Number = y

x + y = 38, or
y = 38 - x..................Eq. 1

4x = 3y - 65..............Eq. 2

Sub 38 - x from Eq. 1 for y in Eq. 2:

4x = 3(38 - x) - 65
4x = 114 - 3x - 65
4x + 3x = 114 - 65
7x = 49
x = 49 / 7
x = 7

and

y = 38 - 7
y = 31

The numbers are 7 and 31.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

x + y =38

4x + 65 = 3y

Plug and chug...

4x + 65 = 3(38-x)

4x + 65 = 114 - 3x

7x = 49

x = 7

y = 31