Solve:One Number Is 6 Less Than A Second Number. Twice The Second Number Is 22 More Than 3 Times The First. Find The Two Numbers?

We can make two equations out of the information provided in the question:

Let's denote the two numbers by x and y:
x = y - 6
2y = 3x + 22

Let's take the variables to one side:
x - y = -6 --- equation I
3x - 2y = -22 --- equation II

Multiply Equation I by -2:

-2 (x - y = -6)
-2x + 2y = 12 --- equation III

Now, we can solve equation II and III as simultaneous equations:

3x - 2y = -22
-2x + 2y = 12
x + 0 = -10
x = -10

To find y, put the value of x into equation II:
3x - 2y = -22
3(-10) - 2y = -22
-30 - 2y = -22
-2y = -22 + 30
-2y = 8
y = 8/-2
y = -8/2
y = -4

Therefore, the two numbers are:
x = -10
y = -4