Question

The sum of 2 numbers is 9 and the difference is 5

Answer 1

Answer:

THE TWO ARE NUMBERS ARE

2 AND 7

Step-by-step explanation:

Personally, I think one variable is easier, but I'll show you both.

1. ONE variable

"two numbers WHOSE SUM IS 9"

x = one number

9 - x = other number (since the sum of the two numbers is 9, and one of them is x, then the other number would be the remainder or the difference when x is subtracted from 9

"the difference is five"

(9 - x) - x = 5

9 - x - x = 5

9 - 2x = 5

Subtract 9 from both sides: -2x = -4

Divide both sides by -2: x = 2

One of the numbers is 2. Plug this into the expression for the other number to find the other number.

9 - x

9 - 2

7

***THEREFORE, THE NUMBERS ARE 2 AND 7.

2. TWO variables

x = one number

y = other number

"whose sum is 9"

x + y = 9

"and the difference is five"

x - y = 5

Solve as a system of equations by "adding" the two equations.

x + y = 9

+(x - y = 5)

-----------

2x + 0y = 14

2x = 14

x = 7

Plug this value for x into either of the two equations and solve for y to find the value of the other number.

x + y = 9

7 + y = 9

y = 2

***THEREFORE, THE NUMBERS ARE 2 AND 7

Answer 2

Answer:

The numbers are 2 and 7.

Step-by-step explanation:

If x and y are the 2 numbers:

x + y = 9

x - y = 5       Adding the 2 equations

2x + 0 = 14

x = 7.

Plug this into the first equation:

7 + y = 9

y = 2.