Question

Two numbers have a sum of 19 and a difference of 5. Find the two numbers

Answer 1

So for this, we will be doing a system of equations, one equation representing the sum and the other representing the difference. Let x = larger number and y = smaller number:

`x+y=19\\ x-y=5`

For this, I will be using the elimination method. With these equations, add them together to get
`2x=24` . From here we can solve for x.

For this, just divide both sides by 2 and your first answer is
`x=12`

Now that we have the value of x, substitute it into either equation to solve for y:

`12+y=19\\ y=7\\ \\ 12-y=5\\ -y=-7\\ y=7`

In short, the two numbers are 12 and 7.

Answer 2

Let "x" represent the first number and "y" represent the second number.

Set up a system of equations, solve one of the variables using any method (I will be using the elimination method), and then plug that solution into either equation to solve for the remaining variable.

x + y = 19

+ x - y = 5

2x = 24 added the equations to eliminate "y"

x = 12 divided both sides by 2

12 + y = 19 substituted "x = 12" into the first equation

y = 7 subtracted 12 from both sides

Answer: 12 and 7