The difference of two numbers is 9 the sum is 11 what are the two numbers

Answer 1

10 and 1 sum to 11

10-1 = 9

x+y = 11

x -y= 9

add

2x =20

x = 10

y = 11-10 = 1

10 and 1, assuming the decimal system, base 10

Answer 2

This problem tackles systems of equations, and so

We want to begin by writing two separate equations using two separate variables to represent the unknown numbers.

k+n = 11

k-n = 9

We then want to chose one equation and one variable from the equation to isolate. So here I am going to chose variable k in the difference equation to isolate.

The equation should now look like :

k = n +9

We then want to substitute in the entire right side of the difference equation ( n+9) for k in the sum equation, thus giving us one equation and one variable to solve for

n+9+n = 11

Then we combine like terms and solve for n

2n+9= 11

subtract 9 from both sides

2n = 2

divide both sides by 2

n=1

substitute n back into either the sum or difference equation to solve for k

k+n = 11

k +1 = 11

subtract one from both sides

k = 10