If x+y =40 and xy = 384 what are the values of x and y?

Answer 1

You may use either equation to eliminate a variable in the other equation.

Since xy = 384, then x = 384/y

Put that into the other equation:

x + y = 40

384/y + y = 40

384 + y2 = 40y [multiply all by y

y2 - 40y + 384 = 0

(y - 24)(y - 16) = 0 [either facror or use Quadratic Formula]

Either y = 24 or y=16 [Multiplicative property of zero]

So, these two solutions are:

1) x = 24 and y = 16

and

2) x = 16 and y=24

Check (very important):

1) Does x + y = 40 ?

24 + 16 = 40 ?

40 = 40 ?yes

Does xy = 384 ?

24*16 = 384 ?

384 = 384 ?yes

2) Does x + y = 40 ?

16 + 24 = 40 ?

40 = 40 ?yes

Does x*y = 384 ?

16*24 = 384 ?

384 = 384 ? yes

Answer 2

Greetings! Lets solve this shall we ?

Lets solve x + y = 40 for y such that y = -x + 40. Then, substitute this y into xy = 384 so we can find these missing numbers! Then,

x(-x+40) = 384...............Distribute the x inside using the Distributive Property such that

-x²+40x = 384................Lets add the x² term over to the left side because we dont want to deal with an negative leading coefficients such that

x²+384 = 40x..................Now lets subtract 40x to the left side such that putting it into quadratic form such that

x²-40x+384 = 0..............Now we must factor it by finding two numbers multiplying to get 384 and adding to get -40. We notice those two numbers are -16 and -24... These two integers multiply to get us +384 and adds together to get -40. Then,

(x-16)(x-24) = 0......................Now we use the Zero-Product Property to get

x - 16 = 0 and x - 24 = 0.................Solving each one for x gets us

x = 16 and x = 24.

Hence x = 16 and y = 24

These two numbers are the answers for x and y even though it factored into two x values.

I hope this helped!

Answer 3

Factoring 384 will work here

You could use a substitution but factoring may still be required

So I'd recommend two digit numbers as factors since single digits would make this a very long way around.

Even numbers are also highly recommended this should also save some time.

Give it a try.

I got 24 and 16 by factoring

Answer 4

20*20=400

21*19=399

22*18=396

23*17=391

24*16=384 (-24)(-16)

Answer 5

if x + y = 40

xy = 384 then y = 384/x

substituting into the first equation, x + 384/x = 40 or x² + 384 = 40x rearranging we get

x² -40x + 384 = 0 The quadratic equation tells us that

x = 24 or 16.

Answer 6

x + y = 40

y = 40 - x

x(40 - x) = 384

40x - x² = 384

0 = x² - 40x + 384

Can you factor and solve?