The difference between two integers is 13 and their sum is 87. What are the two integers?

Question

johnweldon1993 · Answer

Let the first integer = x   and the second = y

$$\large x - y = 13$$
$$\large x + y = 87$$

What would be done next?

andpeggy · Answer

would you solve by solution/substitution?

johnweldon1993 · Answer

You can either do substitution or elimination

*Note that here elimination works much quicker..simply add the 2 equations

andpeggy · Answer

so using elimination it would turn out being 2x+2y=100 or is that incorrect?

johnweldon1993 · Answer

Not quite

When you do: x + x you do indeed get 2x

However..what is -y + y ?

andpeggy · Answer

0

johnweldon1993 · Answer

Exactly! So by adding the 2 equations we have a resulting equation of

$$\large 2x = 100$$

meaning x = ?

andpeggy · Answer

x=50

johnweldon1993 · Answer

Good! Anddddd y = ?

andpeggy · Answer

wasn't it 0?

johnweldon1993 · Answer

it WAS when we combined the equations...however now, go back to the original equations

You now know x = 50...so what does 'y' equal in order to satisfy the original equations?

andpeggy · Answer

is it 1?

johnweldon1993 · Answer

$$\large x - y = 13$$
$$\large x + y = 87$$

We know x = 50...what does y = ?

andpeggy · Answer

y=37