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

add all the numbers and check the ones place.

the answer is 486. as the ones place is more than 4, the estimation will be the next 10 ie, 490