Question

The system of equations 4x - y = 4( x + 1) y = 6 has_____________.

Answer 1

Interpreting the system as
4x − y = 4
(x + 1)y = 6

From the first, y = 4x − 4. Substitute into the second:
(x + 1)(4x − 4) = 6 → 4(x^2 − 1) = 6 → 4x^2 = 10 → x^2 = 5/2 → x = ±√(5/2) = ±(√10)/2.

Then y = 4x − 4, so the two solutions are
(x, y) = (√10/2, 2√10 − 4) and (−√10/2, −2√10 − 4).

Thus the system has two real solutions.