Which systems of equations have no real number solutions? check all that apply. y = x2 + 4x + 7 and y = 2 y = x2 – 2 and y = x + 5 y = –x2 – 3 and y = 9 + 2x y = –3x – 6 and y = 2x2 – 7x y = x2 and y = 10 – 8x

QUESTION 1

The first system is

and

Let us equate the two system to obtain,

Let us rewrite in general quadratic format to get

This implies that,

We now find the discriminant,

Since the discriminant is negative, the system has no real number solution.

QUESTION 2

The second system is

and

We equate the two system to obtain,

This implies that,

We substitute the values to obtain,

Since the discriminant is positive, the system has real number solutions.

QUESTION 3

The given system is

Equate the system to get,

Rewrite in general quadratic format

Divide through by -1 to get,

Using the discriminant we obtain,

Since the discriminant is negative the system has no real number solution.

QUESTION 4

The given system is,

and

Equate the two equations to get,

Rewrite in general quadratic format, to obtain,

Divide through by 2 to obtain,

This implies that,

We calculate the discriminant to obtain,

Since the discriminant is negative the system has no real number solution.

QUESTION 5

The given system is

and

Equate the two equations to get,

Rewrite in general quadratic format to obtain,

We now calculate the discriminant to get,

Since the discriminant is positive the system has real number solutions.