待定系数法8+2D-2E+F=0.36+5D+3E+F=0.10+3D-E+F=0应该怎么解出DEF.怎么消元的.

题目

待定系数法8+2D-2E+F=0.36+5D+3E+F=0.10+3D-E+F=0应该怎么解出DEF.怎么消元的.
{8+2D-2E+F=0}
{36+5D+3E+F=0}
{0+3D-E+F=0}

答案

{8+2D-2E+F=0 ①
{36+5D+3E+F=0 ②
{0+3D-E+F=0 ③
③-①得 -8+D+E=0 ④
②-①得 26+3D+5E=0 ⑤
解④、⑤得D=33、E=-25
把D=33、E=-25代入③得F=-124
所以方程组的解是
{D=33,
{E=-25
{F=-124