How many real solutions does this system of equations have? xy = 9

y = 3x - 1

two real, unequal roots

Step-by-step explanation:

y is definied as y = 3x - 1. Substitute 3x - 1 for y in xy = 9, obtaining:

x (3x - 1) = 9. Then:

3x^2 - x - 9 = 0. In this quadratic, the coefficients are a = 3, b = - 1 and c = - 9.

Calculating the discriminant b^2 - 4ac, we get (-1) ^2 - 4 (3) (-9), or 1 + 108, or 109. Because the discriminant is positive, we have two real, unequal roots.