Question

Write a system of equations that represents the given equation then find the two numbers

The sum or two numbers is 68. The difference is 12

Answer 1

40 and 28

Explanation:

We have two unknown numbers, so let's call them x and y for now.

We know the sum of the two numbers is 68, and the difference is 12, so let's substitute those two numbers for x and y:

x+y=68

and

x-y=12

Because both of these systems are true, we can take both these equations and combine them, by adding each side of one equation with the corresponding side of the other.

So we have:

(x+y)+(x-y)=(68)+(12)

2x=80

x=40

Now we know one of the numbers, x, is equal to 40, so now we can plug that number back into one of the two original equations, x+y=68 or x-y=12. I'll choose x-y=12.

After plugging in x, we get:

40-y=12

-y=-28

y=28

So now we have figured out x and y, which are 40 and 28.