Question

WILL GIVE MEDALS!! what is the solution set to the following system?
{x+y=5
{x^2+y^2=25

Answer 1

@mathmale can you help

Answer 2

solve for either x or y in the first equation and then plug that into the second

Answer 3

Hi, DB,
Paul is right. Why not solve the first equation for y (in terms of x), and substitute that formula for x where x appears in the second equation?

Answer 4

idk if it's (0,5),(-5,0) or (0,5),(5,0)

Answer 5

I see. Were those to be your final answers? Or just intermediate steps?

Answer 6

final answer

Answer 7

What I was suggesting just a moment back, was that you solve x+y=5 for y; all you have to do is to subtract x from both sides of that equation. Then y=5-x.

Subst. that into the other equation. You'll get:

Answer 8

\[x ^{2}+y ^{2}=25\rightarrow(5-y)^{2}+y ^{2}=25.\]

OK. Looks like I may be repeating what you've already done. Let's go back and check each of those points and see whether any of them satisfy both of the given equations.

Answer 9

it can be both of those answers

Answer 10

Starting with (0,5): let x=0 and y=5. Then both equations are true. (0,5) is a solution.

Answer 11

Next, test (-5,0). x=-5 and y=0. The first equation is no longer true, correct? So, eliminate (-5,0) as a solution.
Make sense?
Now

Answer 12

would you please check out the two remaining possible solutions that you typed earlier. Which one is a solution? which one is not a solution?

Answer 13

yes i got it the answers is (0,5)(5,0)

Answer 14

So the key to solving this problem was to double check each of the four points you identified as possible solutions and to eliminate those that do not satisfy the original equations.
Good going! Hope to "see" you again soon online. MM

Answer 15

PS: If you were to draw the circle x^2 + y^2 = 25 and then draw x+y=5 on the same set of axes, the solutions would be immediately obvious.