the sum of two numbers is 14 and their difference is 8

Question

what are the two numbers.

Answer 1

Hi Emily!

To solve this question, we need to set up a system of equations based on the information given. We will call the numbers x and y. Based on the information give, we know that the sum of the numbers is equal to 14 or:

x+y=14

And the difference of the two numbers is 8 or:

x-y=8

So we have to solve one of the equations for x in terms of y and then plug it in to the other equation. If we solve the second equation for x by adding y to each side of the equation, we get: x=8+y

Then we can plug that into the first equation for the value of x:

x+y=14 becomes (8+y)+y=14 or 8+2y=14,

Subtracting 8 from each side of the equation we get 2y = 6

Dividing each side of the equation by 2, we get y =3

Now that we know y=3, we can plug that in to either of the equations to solve for x. Because we already know that x =8+y, when we plug in 3 for y, we get: x = 8+3

x=11

Now that you have these values, it is important to plug them into both equations to check your work. Hope this helps!