Question

19．求$\left\{\begin{array}{l}{5x+7y+3z=25}\\{3x-y-6z=2}\end{array}\right.$的自然数解．

Answer 1

分析 根据解方程的方法和题意可以解答本题．

解答 解：$\left\{\begin{array}{l}{5x+7y+3z=25}&{①}\\{3x-y-6z=2}&{②}\end{array}\right.$
①+②×7，得
26x-39z=39，
∴26x-39z=39的自然数解是$\left\{\begin{array}{l}{x=3}\\{z=1}\end{array}\right.$，
将$\left\{\begin{array}{l}{x=3}\\{z=1}\end{array}\right.$代入①，得
y=1，
故$\left\{\begin{array}{l}{5x+7y+3z=25}\\{3x-y-6z=2}\end{array}\right.$的自然数解是$\left\{\begin{array}{l}{x=3}\\{y=1}\\{z=1}\end{array}\right.$．

点评 本题考查解三元一次方程组，解题的关键是明确解三元一次方程组的方法．