Question

Let c be a constant. For what values of c can the simultaneous equations x – y = 2; cx + y = 3 have a solution (x, y) inside quadrant I

Answer 1

we need x>0 and y>0
eliminating y, we have

x-(3-cx) = 2
(c+1)x = 5
c+1 > 0
c > -1

eliminating x, we have

cx-cy = 2c
cx+y = 3

(1+c)y = 3-2c
y = (3-2c)/(c+1)
since c+1 > 0, 3-2c > 0, so c < 3/2

so, -1 < c < 3/2