Question

In the following equations y = 23/x and y = -x - 5, what are the values of x and y that simultaneously satisfy both of these linear equations?

A. (0, -5)
B. (6, 1)
C. (-6, 1)
D. (5, -6)

Answer 1

There are no values of x and y that simultaneously satisfy both equations.

Step-by-step explanation:

To find the values of x and y that simultaneously satisfy both equations, we can set the equations equal to each other:

23/x = -x - 5

To solve this equation, we can multiply both sides by x:

23 = -x^2 - 5x

Next, we can rearrange the equation into standard quadratic form:

x^2 + 5x + 23 = 0

Using the quadratic formula, we can find the values of x that satisfy this equation:

x = (-5 ± √(5^2 - 4*1*23)) / (2*1)

x = (-5 ± √(-67)) / 2

Since the discriminant (√(-67)) is an imaginary number, there are no real solutions for x that satisfy both equations. Therefore, there are no values of x and y that simultaneously satisfy both equations.