Question

How many real solutions does this system of equations have? xy = 9 y = 3x - 1

Answer 1

Answer:

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.