10. Mother's Day is here, and Xiao Hong, Xiao Li, and Xiao Ying go to a flower shop to buy flowers for their mothers. Xiao Hong bought 3 roses, 7 carnations, and 1 lily, and paid 14 yuan; Xiao Li bought 4 roses, 10 carnations, and 1 lily, and paid 16 yuan; Xiao Ying bought 2 stems of each of the above flowers. Then she should pay $\qquad$ yuan.
10. 20 .

Let the unit prices of roses, carnations, and lilies be $x$ yuan, $y$ yuan, and $z$ yuan, respectively. Then
$$
\left\{\begin{array}{l}
3 x+7 y+z=14, \\
4 x+10 y+z=16
\end{array}\right.
$$

Eliminating $z$ gives
$$
x=2-3 y \text {. }
$$

Substituting equation (2) into equation (1) gives
$$
z=8+2 y \text {. }
$$

From equations (2) and (3), we get
$$
x+y+z=10 \Rightarrow 2(x+y+z)=20 \text {. }
$$

Therefore, Xiaoying should pay 20 yuan.