11. The number of solutions to the following system of equations
y^{2} – xy - |x|y + x|x| = 0
x^{2} + y^{2} = 1
is
A. 0 |
B. 1 |
C. 2 |
D. 3 |
E. 4 |
Solution: The answer is D
The first equation factors:
Thus the values satisfying the first equation are the points (x, y) That fall on the lines y = x or y = |x|. Note that the line for y = x coincides with y = |x| for x >= 0. The lines y = x and y = |x| are different, however, when x < 0.
Consquently, the line y = x intersects the circle x^{2} + y^{2} = 1 at two points, one in the first quadrant and one on the third quadrant. The line y = |x| will have an additional point of intersection in the second quadrant