Question

已知方程组{X+2Y=1－M 2X+Y=1+3M的解满足X+Y≥1,求M的取值范围.

Answer 1

∵方程组X+2Y=1－M, 2X+Y=1+3M ,∴解得：x=(1+7M)/3,y=(1-5M)/3,

∵X+Y≥1,∴(1+7M)/3+(1-5M)/3≥1,1+7M+1-5M≥3,

2+2M≥3,2M≥1,M≥1/2.