Question

The sum of the digits of a two digit number is 14. The difference between the tens digit and the units digit is 2.

If x is the tens digit and y is the ones digit, which system of equations represents the word problem?
xy= 14 and x - y= 2
x + y = 14 and x - y= 2
x + y = 14 and y - x= 2

Answer 1

Explanation:

the system of equations representing the word problem is

x+y=14, y-x=2

let x be the tens digit and y be the ones digit

solve simultaneously the two equations,

x+y-x+y=14+2

2y=16

y=8

now put in y=8

8-x=2

x=8-2

x=6

so the digit is 68

Answer 2

see explanation

Explanation:

Sum of the 2 digits x and y is 14, thus

x + y = 14

The difference between the tens digit x and the ones digit y is 2, thus

x - y = 2

The system of equations representing the problem is

x + y = 14 → (1)

x - y = 2 → (2)

Add the2 equations term by term to eliminate y

2x = 16 ( divide both sides by 2 )

x = 8

Substitute x = 8 into (1)

8 + y = 14 ( subtract 8 from both sides )

y = 6

The 2 digit number is 86