Question

How many solutions do these simultaneous

equations have? Give your reason.
x - y = 2
y=x³

Answer 1

The given simultaneous equations can have either one or three solutions.

Step-by-step explanation:

The given simultaneous equations are:

x - y = 2

y = x³

To find the number of solutions, we can rewrite the second equation as:

x³ - y = 0

Now, we can substitute the value of y from the first equation into the second equation:

x³ - (x - 2) = 0

After simplification, we get:

x³ - x + 2 = 0

This equation is a cubic equation, which can have either one or three real solutions. Therefore, the given simultaneous equations can have either one or three solutions.