Question

Consider the following systems of equations:

y=6x^2+1
y=x^2+4

Which statement describes why the system has two solutions?

Each graph has one y-intercept, which is a solution.

Each graph has one vertex, which is a solution.

The graphs of the equations intersect the x-axis at two places.

The graphs of the equations intersect each other at two places.

Answer 1

Hello:
6x²+1 = x²+4
5x² = 3
x² = 3/5
the system has two solutions ( X² =b ..b> 0 has two solutions : ± √b)
x = √(3/5) or x = - √(3/5)
if : x = √(3/5) y = √(3/5) ² +4 =3/5 +4 =23/4
if : x = - √(3/5) y =(- √(3/5)) ² +4 =3/5+4 =23/4
The graphs of the equations intersect each other at two places (points) :
A(√(3/5) , 23/4) and B (-√(3/5) , 23/4)