Question

若方程组3x+y=2k,2y-x=3的解满足x1,求整数k的个数.

Answer 1

3x+y=2k (1)

2y-x=3 (2)

(1)+(2)*3

y+6y=2k+9

y=(2k+9)/6

y>1

(2k+9)/6>1

2k+9>6

k>3/2

x=2y-3=(2k-9)/6

x