Final answer:
To find the values of x and y, we can use the given equations x^2y^2 = 100 and xy = 18. By solving the equations, we find that the possible values of x and y are x = 1 and y = 18/10 or x = -1 and y = -18/10.
Step-by-step explanation:
To find the values of x and y, we can use the given equations. We have x^2y^2 = 100 and xy = 18. Let's solve for x and y using the second equation.
From xy = 18, we can rearrange the equation to get x = 18/y. Substituting this value of x into the first equation, we get (18/y)^2y^2 = 100. Simplifying this equation, we have 324 = 100y^2, which gives us y^2 = 324/100. Taking the square root of both sides, we find y = ±(18/10).
Now, substituting the value of y into the equation xy = 18, we can solve for x. For y = 18/10, we have x(18/10) = 18, which gives us x = 10/10 = 1. For y = -18/10, we have x(-18/10) = 18, which gives us x = -10/10 = -1. Therefore, the values of x and y are x = 1 and y = 18/10 or x = -1 and y = -18/10.