Find the number of solutions to the system of equations y = -x ^ 3 y = -5x.

In order to determine the number of solutions to the system of equations:

y = -x ^ 3;

y = -5x,

let’s solve a system of these equations. And for the solution, we will use the substitution method. Let’s substitute the expression from the second into the first equation instead of the variable y and get:

System of equations:

-5x = -x ^ 3;

y = -5x.

We solve the first equation of the system:

x ^ 3 – 5x = 0;

x (x ^ 2 – 5) = 0;

1) x = 0;

2) x ^ 2 – 5 = 0;

x ^ 2 = 5;

x = √5;

x = -√5.

A set of systems:

System 1:

x = 0;

y = 0;

System 2:

x = √5;

y = -5√5;

System 3:

x = -√5;

y = 5√5.