I can never get word questions right, can someone help? The question states to solve the problem using elimination...

Question

”The sum of the digits of a certain two digit number is 12. The difference of the certain two digit number is 6. What is the number?”

Answer 1

Start with defining the variables.

Let x=the 1st digit

Let y=the 2nd digit

Sum means addition, difference is subtraction. So the 2 equations are:

x+y=12

x-y=6

To do this using elimination, add the equations together. The y and -y will add to zero, so this cancels out. The resulting equation after you add them together is

x+x=12+6 Simplify

2x=18 Divide bother sides by 2 and simplify

2x/2=18/2

x=9

You can use either equation to solve for y next. I will use the first one.

x+y=12 Plug in x=9

9+y=12 Subtract 9 from both sides and simplify

9+y-9=12-9

y=3

The 2 digit number is 93.

Answer 2

let the big no be x and small be y

now according to question,

x+y=12----(i)

x-y=6-----(ii)

now adding both of the equation,

x+ y +x- y =12+6

or, 2x=18

or, x=9

now putting the value of x in eq i

so, 9+y=12

or, y=3//ans