Question

3．已知關(guān)于x的方程組$\left\{\begin{array}{l}{x=2k}\\{x+3y=3k-1}\end{array}\right.$ 的解滿(mǎn)足$\left\{\begin{array}{l}{x＞0}\\{y＜0}\end{array}\right.$，求k的取值范圍．

Answer 1

分析 首先把方程①代入②可得3y=k-1，再由x＞0，y＜0可得不等式組$\left\{\begin{array}{l}{2k＞0}\\{k-1＜0}\end{array}\right.$，解不等式組即可．

解答 解：$\left\{\begin{array}{l}{x=2k①}\\{x+3y=3k-1②}\end{array}\right.$，
把①代入②得：2k+3y=3k-1，
3y=k-1，
∵$\left\{\begin{array}{l}{x＞0}\\{y＜0}\end{array}\right.$，
∴$\left\{\begin{array}{l}{2k＞0}\\{k-1＜0}\end{array}\right.$，
解得：0＜k＜1．

點(diǎn)評(píng) 此題主要考查了解一元一次不等式組，以及二元一次方程組，關(guān)鍵是正確利用含k的代數(shù)式表示x、y．