Question

Xy= -24 , x^2+y^2= 52 then x=? y=?

A. x=4, y=-6
B. x=6, y=-4
C. x=-4, y=6
D. x=-6, y=4

Answer 1

By using substitution, the values that satisfy both given equations are x = 4, y = -6 and x = -4, y = 6, with x = 4, y = -6 being the answer if we only consider the provided options.

Step-by-step explanation:

The equations given are xy = -24 and x^2 + y^2 = 52. To solve for the variables x and y, one approach is to express y in terms of x using the first equation and then substitute it into the second equation.

• From the first equation, y = -24/x.
• Substitute y into the second equation: x^2 + (-24/x)^2 = 52.
• Solve for x and then use the value of x to find y.

The correct answers for x and y that satisfy both equations are: x = 4, y = -6 (which corresponds to option A) and x = -4, y = 6 (not listed in the options provided).