设集合A={={(x,y)| 2x-3y=1},B={(x,y)| 2x-y=3},C={(x,y)|ax+y=11},若A∩B=A∩C,求实数a的值
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![设集合A={={(x,y)| 2x-3y=1},B={(x,y)| 2x-y=3},C={(x,y)|ax+y=11},若A∩B=A∩C,求实数a的值](/uploads/image/z/12958847-71-7.jpg?t=%E8%AE%BE%E9%9B%86%E5%90%88A%3D%7B%3D%7B%28x%2Cy%29%7C+2x-3y%3D1%7D%2CB%3D%7B%28x%2Cy%29%7C+2x-y%3D3%7D%2CC%3D%7B%28x%2Cy%29%7Cax%2By%3D11%7D%2C%E8%8B%A5A%E2%88%A9B%3DA%E2%88%A9C%2C%E6%B1%82%E5%AE%9E%E6%95%B0a%E7%9A%84%E5%80%BC)
设集合A={={(x,y)| 2x-3y=1},B={(x,y)| 2x-y=3},C={(x,y)|ax+y=11},若A∩B=A∩C,求实数a的值
设集合A={={(x,y)| 2x-3y=1},B={(x,y)| 2x-y=3},C={(x,y)|ax+y=11},若A∩B=A∩C,求实数a的值
设集合A={={(x,y)| 2x-3y=1},B={(x,y)| 2x-y=3},C={(x,y)|ax+y=11},若A∩B=A∩C,求实数a的值
2x - 3y = 1
2x - y = 3
解得:
x = 2
y = 1
所以 A∩B = {(2 ,1)}
把 (2 ,1)代入 ax + y = 11 得:
2a + 1 = 11
a = 5