Question

How many real solutions does the system have?
Y= -3x-1
Y= x^2 -3x + 4

Answer 1

the system doesn't have any real solutions

Explanation:

Y = -3x-1

Y = x^2 -3x +4

∴ -3x-1 = x^2 -3x +4

x^2 = -5

x = √5 i

Answer 2

No real solution of the given system.

Explanation:

In this question the given equations are y = -3x - 1 and y = x²- 3x + 4.

We have to find the real solutions of the given system.

We will place the value of y from equation 1 to equation 2.

-3x - 1 = x² - 3x + 4

x² -3x + 3x + 4 + 1 = 0

x² + 5 =0

x² = -5

x = √(-5)

Therefore there is no real value of x.

Similarly the value of y of is also not defined.

Therefore there is no real solution for the system which we can see from the graph attached.