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

No real solution of the given system.

Step-by-step 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.

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step-by-step explanation:

answer:   x = 3 + √11     and     x = 3 - √11

step-by-step explanation:

x² - 6x + 9 = 11

(x - 3)² = 11

x - 3 = ±√11

    x = 3 ± √11

x = 3 + √11     and     x = 3 - √11