The sum of two numbers is 19. Their difference is 2. What are the numbers?

Answer 1

One of the fundamental rules of algebra is that if you have n number of variables, you need n number of equations to solve for them.

In this case we have two variables, lets call them x and y, so we'll need a system of two equations to solve for both x and y.

The first step is converting this word problem into math terms.

" The sum of two numbers is 19 " can be written as x+y = 19

" Their difference is 2" can be written as x-y = 2

It doesn't matter which of the two numbers we solve for is x and which one is y, so we just decided to call x the larger number and y the smaller number.

Now in order to solve this we are going to use the substitution method. We are going to look at one of the two equations we have and solve it for one of the variables. We'll then substitute that solution into the second equation. (This will make more sense in a second I promise)

solve equation 1 for x:

x + y = 19

x = 19 - y

substitute solution into equation 2:

x - y = 2

(19 - y) - y = 2

solve second equation for y:

19 - y - y = 2

19 - 2y = 2

-2y = -17

y = 8.5

substitute solution for y into equation 1

x + y =19

x + 8.5 = 19

x = 10.5

The answers to this question are 8.5 and 10.5

we can check these answers by putting them into either of the two equations we made.

Please let me know if that helped or if you need anymore help!

Answer 2

You could also simply add the left sides and right sides of the first 2 equations separately, and set the 2 sums = ,

as follows:

(x + y) + (x - y) = 19 + 2

2x = 21

x = 21/2 or 10.5

Then y = x - 2 = 8.5