х*у=60 х2+у2=169

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To solve this system of equations, you can use the substitution method by isolating one variable in the first equation and then substituting it into the second equation. Let's solve it step by step:

From the first equation, we have
х*у = 6
у = 60/х

Substitute у = 60/х into the second equation
х^2 + (60/х)^2 = 16
х^2 + 3600/x^2 = 16
Multiplying through by x^2, we get
x^4 + 3600 = 169x^
Rearranging terms, we get
x^4 - 169x^2 + 3600 = 0

Now, let's solve this equation for x. This equation is a quadratic in terms of x^2, so let's make a substitution
Let u = x^
Then the equation becomes
u^2 - 169u + 3600 =
(u - 25)(u - 144) =
u = 25 or u = 144

Substitute back u = x^2
Case 1: u = 2
x^2 = 2
x = ±5

Case 2: u = 14
x^2 = 14
x = ±12

Now that we have the possible values for x, we can find the corresponding values for у using у = 60/х
For x = 5: у = 60/5 = 1
For x = -5: у = 60/(-5) = -1
For x = 12: у = 60/12 =
For x = -12: у = 60/(-12) = -5

Therefore, the solutions to the system of equations are
(x, у) = {(5, 12), (-5, -12), (12, 5), (-12, -5)}