Help with math

The question: Where do x and y cross? I don't really care about the answers, I just want to know how to solve it.

 

I am assuming you are done since this looked like a homework problem but just in case here is the answer. You can use two different strategies, Substitution or Combination. You will learn which method is fastest or easiest with practice.

For the these problems I would use substitution. I will show you the beginning of the first problem.

EQUATION A: (x^2) + (y^2) = 25
EQUATION B: 3x + y = 5

First subtract 3x from both sides of equation B.

EQUATION B: y = 5 - 3x

Now since each side is equivalent, substitute 5 - 3x in for y in equation A.

EQUATION A: (x^2) + (5 - 3x)^2 = 25

Now solve for x. Then plug your x into either equation and solve for y.

 

Thanks for the help. I was still trying to find a way to solve it. Found the coordinates (0, 5) and (3, -4).

3x + y = 5
y = 5 - 3x
x^2 + (5 - 3x)^2 = 25
x^2 + 9x^2 - 30x + 25 = 25
10x^2 -30x = 0
x^2 - 3x = 0
x(x - 3) = 0
x = 3 or x = 0
3 x 3 + y = 5 or 3 x 0 + y = 5
9 + y = 5 or y = 5
y = -4 or y = 5
(3, -4) or (0, 5)

Look right?


Can this method used in the second graph? You would get:
xy = 8
x = 8 / y
(8 / y)^2 + y^2 = 20
64 / y^2 + y^2 = 20
64 / y^2 = 20 - y^2
64 = 20y^2 - y^4
y^4 - 20y^2 + 64 = 0
p^2 - 20p + 64 = 0 (x^2 = p, easier to calculate)
(p - 16)(p - 4)
p = 16 or p = 4
x^2 = 16 or x^2 = 4
x = 4 or x = -4 or x = 2 or x = -2
(4, 2) or (-4, -2) or (2, 4) or (-2, -4)