Question

How many real solutions does the system have? {y=−3x−3y=x2−3x+5 Enter your answer in the box

Answer 1

Zero real solutions does the system have.

Explanation:

Given the system of equations:

`y = -3x-3`

`y = x^2-3x+5`

Equate these equations we have;

`-3x-3 = x^2-3x+5`

Add 3x to both sides we have;

`-3 = x^2+5`

Subtract 5 from both sides we have;

`x^2 = -8`

⇒
`x = \pm √(-8)=\pm 8i`

`x = \pm 8i`, where i is the imaginary part.

both solution are imaginary.

Therefore, the system of equation does not have any real solutions.

Answer 2

we have that
y=−3x−3
y=x²−3x+5

using a graph tool
see the attached figure


the system has zero real solutions, the graphics do not intercept