Question

A为和值时,方程组2X-3y=a+1和x+2y=a的解满足xy均为正数?

Answer 1

2x - 3y = a+1

x + 2y = a

2x - 3y = a+1

2x + 4y = 2a

下面式减上面式子 消 x

7y = a -1

y = (a-1)/7

x = a - 2y = a - 2(a-1)/7 = (5a +2)/7

x>0

y>0

5a + 2>0

a-1>0

a > -2/5

a > 1

所以 要使 x y 均为正数,则 a > 1