One number is two less than a second number. twice the first is 10 more than 4 times the second. find the numbers. the value of the first number is nothing.

12 more than 6 time the second

Step-by-step explanation:

Here's how to translate from English to algebra

one number   IS    two less than another

         X          =               Y-2

twice the first    is     12 more than    6 times the second

       2x             =          12  +               6y

2 x     = 6y +12 <--- commutative property of subtraction; can switch them

2(y-2) = 6y + 12 < substitutes the first equation into the second

2y - 4 = 6y + 12 <--- distributive left side

0 = 6y + 12 - 2y + 4   < everything to the right side; changes signs in the process

0 = 4y + 16         <--- combines like terms

-16 = 4y  <--- subtracts 16 from both sides

y  = -4  <--- divides both sides by 4

Then

x = -4 - 2 = -6

CHECK:

    y - 2 = -4 - 2= -6 = x  <--- yes, it works; one number is 2 less than the other.

   2(-6) = 12 + 6(-4)  ---> -12 = 12 + -24 ; yes it works!! twice the first is in fact 12 more than 6 time the second