Question

How many real solutions does the system have? y=−3x−1y=x2−3x+4?

Answer 1

Set the equations to equal each other:
x²-3x+4=-3x-1
x²-3x+3x+4=-3x+3x-1
x²+4=-1
x²+4-4=-1-4
x²=-5
√x²=√-5
x=-√5i and x=√5i

There are no real solutions.