Question

What is one of the solutions to the following system of equations?

y2 + x2 = 53
y − x = 5

(−10, −5)

(−7, −2)

(7, 2)

(5, 10)

Answer 1

@dumbcow

Answer 2

okay, you can solve this by substitution.

y^2 + x^2 = 53
y - x = 5

solve the second equation for x or y. plug the result into the first equation. that should give you an equation in just one variable. solve it.

Answer 3

Two negatives make a positive

Answer 4

@MountainDew is guessing. you need to do what I said.

Answer 5

I think its a because -10 - -5= 5

Answer 6

Im not guessing I had to look for a second

Answer 7

i tried to understand, and do the equations but i came out with a fraction

Answer 8

here's how you can check your answer.

suppose it is (-10, -5). that means both equations must be correct if you substitute x = -10 and y = -5. Are they?

y - x = 5
(-5) - (-10) = 5
-5 + 10 = 5
well, okay, so far, so good

y^2 + x^2 = 53
(-5)^2 + (-10)^2 = 53
25 + 100 = 53
uh, oops.

Answer 9

A is NOT correct.

Answer 10

i was thinking it was (5,10)

Answer 11

but it came out the same as -10, -5

Answer 12

no more help?

Answer 13

here's how you solve it.

y - x = 5
y^2 + x^2 = 53
solve the first one for y:
y - x= 5
y = x + 5

substitute that into the other equation:

y^2 + x^2 = 53
(x+5)^2 + x^2 = 53
x^2 + 5x + 5x + 25 + x^2 = 53
2x^2 + 10x + 25 = 53
2x^2 + 10x - 28 = 0
x^2 + 5x - 14 = 0

factoring
(x+7)(x-2) = 0
solutions are x = -7, x = 2

so at x = -7, y = x+5 = -2
(-7,-2) is a solution to the system of equations

Answer 14

7.2 is the answer

Answer 15

i then tried 7,2 AND THE first equation did not equal out to be 5

Answer 16

7-2

Answer 17

oh the negative 2 ok i see now

Answer 18

another solution is x = 2, y = x+5 = 7 or (2, 7)

again checking:

x=2, y = 7
x^2 + y^2 = 53
2*2 + 7*7 = 53
4 + 49 = 53
53 = 53

Answer 19

=5

Answer 20

@whpalmer4 gave you the correct answer and the proper method for solving.

Answer 21

(−10, −5)

(−7, −2)

(7, 2)

(5, 10)
those are my possible answers

Answer 22

I said it was b -_-

Answer 23

it's a quadratic equation (has an x^2 in it), so there are two solutions. only one of them is in the answer list.

@MountainDew you were guessing based on your "two negatives make a positive". that would also apply to A, and that was not a solution.

Answer 24

So??

Answer 25

Sorry MountainDew, they say youre wrong :(

Answer 26

I was just trying to help I said maybe

Answer 27

so, the idea here is to show @eliteent how to solve these problems, not how to guess at the answer and get it wrong. doing it correctly is not difficult.

Answer 28

Well at least I tried to help

Answer 29

bro you did good, dont worry about it.

Answer 30

no one is disputing that you tried to help.

Answer 31

Okay bye

Answer 32

This was actually a good question thread because it wasn't just he asker that learned something. :)

Answer 33

Yeah, very nice this website is so elaborately set up. Its very helpful

Answer 34

(-7, -2), (2, 7)